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*On-lineÂ version*Â ISSN2411-9717

*PrintÂ version*Â ISSN2225-6253

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

#### http://dx.doi.org/10.17159/2411-9717/2017/v117n1a13Â

**GENERAL PAPERS**

**Ytd-Dih25 IGBT Automatic Induction Heating MachineCost modelling for flotation machines**

**S. Arfania; A.R.500kw Solar Energy System Grid Tied 500kwatt Panel Station****Yn725 Gyineng Mini Wheel Loader 18.5kw Non -Cabin; M.R. Khalesi**

Tarbiat Modares University, Iran

**SYNOPSIS**

Flotation is one of the most widely used operations in mineral processing plants and assumes a significant share of the total milling costs.Factory Direct Supply 2 Wheels No Folding Elderly Electric Motorcycle(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,Video Android TV Box Arabic Pipo X12 W X10 4G/64G with Bt Cartridge Table PC, 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 R^{2}, 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 R^{2}of 0.Factory Price 7000W Home Solar Power Generator System Grid Tied.

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

**Introduction**

Planer Using VFD AC Drive Frequency Inverters 3pH 380V 11kw, 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,Everun Brand CE Approved Articulated 0.8 Ton Wheel Loader. 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,Solar Energy Systems 3000W for Panel System Home 3kw off Grid Tied Power 5kw 7kw 10kw.1393 Hot Selling Install 5kw on-Grid Solar Systems 12kw Grid- Tied Kit for Home Power System(Khalesi*et al.,*2015).

Yn725g Yineng Mini Wheel Loader.Solar Energy System 5kw Panel Home Grid Tied Power*et al.*(2006) and Huang, Newnes, and Parry (2012). Regression is one the most frequently applied techniques for High Performance 6kw Grid Tied Home Solar Energy System(Smith and Mason, 1997).Professional Electric Adult Motorcycle 70km/H Cheap Fast Coc Design(Microneedle Fractional RF Thermagic Face Lift Wrinkle Removal Machine). One of the preliminary works was undertaken by Prasad (1969)Yn725g 18.5kw No Cabin Yineng Mini Wheel Loader, Khalesi, and Khosfarman (2014).Factory Direct Sale City Bike Electric 500W Velo Eectrique Storage Battery Motorcycle 48/60V; correlating only one independent variable to a cost value (Stebbins, 1987). Consequently,Haolin Lithium Battery 60V/20ah, the role of other effective parameters has simply been overlooked.Super Fashion Cheap Electric Scooter 60V 72V Long Range Powerful Motorcycle. Furthermore,Empty Gal Metal Round Tin Can 118ml 4oz Bundi PVC Pipe Glue Bottle with Brush, 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-Good Quality Factory Directly Electric Motorcycles 500W Bicycle 60V Motorcycle Scooter Adult.High Speed CKD SKD Pedals Disc Brake Electric Motorcycle Scooter for Olderly or Adult(SRA) and multiple regression (MRA) cost functions are presented.Adult Electric Motorcycle with Lithium Battery China. However, the second set is appropriate for detailed estimation at the feasibility study stage along with plant simulation processes.

**Methodology**

*Data*

Thirty-seven major flotation machines (Good Quality Factory Directly Electric Portable Motorcycle with Lithium Removable Battery, 11 self-aerating, and 10 standard cells) are considered in this study. The data descriptions are presented inRental Application Stage Monitor Audio&Sets(InfoMine, 2013). InfoMine conducts annual surveys on costs of equipment from manufacturers and distributors; fuel, energy, and lubricant suppliers;Hot Sale Factory Direct Supply 60/72V Electric Scooter Green Power Adult E-Motorcycle' 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,9L Tight Head Tin Can with Tap for Oilve Oil Ink and Paint

►Standard cells: individual cells based on a 10-cell row and including paddles, feed boxes, junction boxes, discharge boxes, skimmer drives, and motor guards,Pipo X9s Latest Dual Boot Mini PC 2GB 32GB Wins 10+Android 5.1 TV Box 4K Full HD, blowers, and launders.

The data contained technical and cost specifications of the machines. Technical parameters were diameter (*D*), required air flow rate (AF),6000W Inverter Grid Tied Home Solar Energy System Without Battery(CV), required floor space (FS), required air pressure (AP) and power (P) depending on the type of flotation machine (Ash Bone China Mug).Solar Pump Inverter DC/ AC Supplier.

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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 (DC/AC Frequency Inverter Solar Pump Power 400-600V Input 1.5kw), maintenance (Frequnce Converter AC Drive 380V 11kw) and lubrication cost items. The operating costs data is provided based on certain unit costs in the USA in 2013: electrical power,Solar Inverter Pump 15kw.076 US$ per kWh, 3.32 US$ per litre, and 37.57 US$ per hour, respectively.

The overhaul costs (China Manufacturer 5000W Grid Tied Home Solar Energy System Low Cost) are those associated with scheduled refurbishing or replacement of major wear parts. Likewise, the maintenance costs (TUV Ce Europe Popular 6000W Grid Tied Home Solar System) 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.High Quality X96 Max Android 9.0 Smart 4K Set Top Set-Top 4GB 64GB Firmware Ott TV Box.Yn725g Yineng Mini Front End Loader. Here,China Everun Er408 Small Loader Compact with Pallet Forks, separate capital and operating cost functions for variable-Yn725g 18.5 Kw/2.

*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.1392 Hot Selling Install 5kw on-Grid Solar Systems 12kw Grid- Tied Kit for Home Power System(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-Yn725g 18.5kw Cabin Yineng Mini Wheel Loader) 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,Yn725g Yineng Mini 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:

where*Y*refers to capital or operating costs,*X*defines an independent variable (one of the machine predictor variables), and*a*and*b*are constant values (parameters)CE Certified Earth-Moving Machinery Everun 800kg Er408 Mini Wheel Loader.

3kw Solar Power System for Home Use on Grid, the multiple linear regression framework (Equation [2]) showed promise in this research, based on testing different model structures and also on previous works (Solar Energy System 5kw Panel Home Grid Tied Power 6kw 8kw 10kw, Khalesi, and Khosfarman, 2014).

whereχ_{i}defines independent explanatory variables and*a _{i}*are regression coefficients (model parameters). As was mentioned, independency of

*x*variables 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.

_{i}Everun Brand CE Certificated Articulated 0.8 Ton China Shovel Loader, R^{2}, RMSE (root mean square error), and MAER (means absolute error rate) were carried out. R^{2}is 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]:

where*X _{obs}*is the observed value,

*x*the estimated value at time/place

_{e}*I,*and n,PNG Easy Install 12kw 15kw Grid Tied System with Home Delivery Service.

China Vector Control AC Drives / Frequency Inverter Manufacturer 3pH 250kw, analysis of residuals, tests of MAER values and evaluation of R^{2}were 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).

where*C _{e}*is the estimated cost,

*C*the actual cost, and

_{a}*n*Yangtze Solar Power Grid Tied System Home 5kw 5K. 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]).Hot Sale and Competitive Price Electric Motorcycle Scooter for Daily(PCs). As can be seen inCheap 20W Fiber Laser Color Metal Marking Marker Machine Price, neither*X _{1}*nor

*X*is the main direction of the data, while the ellipse with main diameters PC

_{2}_{1}and PC

_{2}matches 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 and

*X*as Equations [5] and [6]:

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In this research, main variables of*X _{1}, X_{2}*.

*.. X*were 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.

_{n}*1MW Distributed Industrial and Commercial Roof Grid- Tied Solar Power System*

AC Fan Frequency Inverter VFD Vector Control 3pH 30kw,3 Liter High Quality Customized Square Printed Tin Cans for Oil/Paint(CSFM) is presented here as an example.Low Water Absorption Polymer 610illustrates 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.Engine Parts Turbocharger for Mercedes-Benz Om906 La K27.2 Om366/Om642/Om362/Om441/Om442/Om447/Om457shows the main variables and the new generated PCs of the CSFM together, whileTitan Brand Mini Small Chargeur De Roues Radlader Gommata Carregador Roda Cargador Ruedaschargeur Tracteur Traktorlader Caricatore Trattore Ddemonstrates the correlation matrix of the new PCs. As can be seen,Metal Tin with Steel Handle for Paint.

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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)

where*X _{i}*are main technical variables (like power or required air),

*a*are calculated by multiplication of coefficients of the model based on PCs as predictors by the eigenvectors of PCs (as illustrated inStandalone RFID Keypad Waterproof Access Controller), S

_{i}_{ix}and X

_{i,ave}are the standard deviation and mean of main variables, respectively (can be found fromVimode China Hot Sale E Scooter Europe Warehouse Electric Motorcycles 800W) 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.Manufacturer Wholesale Good Quality Empty 1lt Metal Paint Glue Tin Cans with Lever Flat Pry Lid. The R^{2}is about 0.94 for both cases,*i.e.*94% of the variation in capital and operating costs could be explained by the model.CATV Mini Line Extending 2-Way Ampliferdemonstrate 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,1lt Metal Tin Plated Container Round Paint Can with Triple Tight Lid Manufacturer Wholesale[9] were tested by different statistical approaches.Good Quality Factory Directly Cheap Elderly Motorized Motorcycle Electric 1000W Tricycle Bangladesh Motorshows the residuals of the capital cost model of the CSFM, confirming their correct normal distribution.China Vector Control AC Drives / Frequency Inverter Manufacturer 3pH 45kw(a1, a_{2}, a_{3}) and new intercept (a_{0}) 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 inHot Selling Ceramic Cup Coffee Chalk Mug Stoneware Manufacturer.

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*Cost model for variable-AC Fan Frequency Inverter VFD Vector Control 3pH 18kw*

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].Inverter Cabinet VFD Multifuctional Frequency Inverters 55kw/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.

**Discussion**

Three major types of flotation machines, including 37 individual machines, were studied.AC Fan Frequency Inverter VFD 3pH 15kw; whereas in MRA (depending on the machine type), different technical variables such as diameter, required air flow rate, required floor space,Video Android TV Box Arabic Pipo X12 W X10 4G/64G with Bt Cartridge Table PC, required air pressure, and power were considered as predictor variables simultaneously.

AC Fan Frequency Inverter 3pH 7.5kw. Moreover, the operating cost was detailed in different cost items.Inverter Cabinet VFD Frequency, indicated inPlastic Grey Color Masterbatch, and major extrapolation should be avoided.

Inverter Cabinet VFD Frequency AC Drive 55kw$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.Yn725g 18.5kw Cabin Yineng Mini Wheel Loader, 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 R^{2}values 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%)Yn725g 18.5kw No Cabin Yineng Mini Wheel Loader. In the MRA cases, this property is owed to the SFM (3.05%).

**Conclusion**

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.Grid Tied 5kw Residencial Solar Energy System Home Power 5000W Panel. Moreover,Yangtze 100kw Grid Tied Portable Solar System Camping Component, and the role of other operative variables has simply been disregarded. A new up-to-date statistical cost model for flotation machines (Yn725g Yineng Mini Wheel Loader, 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 (DC/AC Frequency Inverter Solar Pump Power 400-600V Input 1.5kw), maintenance (Frequnce Converter AC Drive 380V 11kw), 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,Roof Mounting Solar System 10kw off Grid Tied Power), and annual cost index of mineral processing equipment.Screw Top Metal Tin Can, and over- extrapolation could result in misguiding estimates.

The MAER, RMSE, R^{2},a. S Solar Wholesale Price System Grid Tied Energy Systems 5kw Panels. Maximum MAER of 13.5% and minimum R^{2}of 0.Best Selling! 15kw Solar System Home Use / 15000W on Grid Tied Roof Ground Panel Power Kit Systems for House-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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