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


2500*640mm E1 Glue Engineer Veneer Wenge/Oak for DecorationCost modelling for flotation machines

S. Arfania; A.R.Factory Price Power Battery Motor E Scooter 60V 20ah 2000W Electric MotorcycleIron Oxide Yellow for Pet Feeds; 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.Electric Motorcycles Adults Powerful Racing Motorcycle for Adult 1000W 60V/72V in Warehouse(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,Frequency Drive Converter Solar Pump 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.China E Bike Electric Bicycle 48V 20A Ebike Nakto Motorcycle.

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


60V 800 Watt 150kg Load Electric E Bike Motorcycle Moped 45 Km H for 2 Person Adults UK, 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,Adult Electric Motorcycle/Electric Bike/E-Bike W Waterproof with Double Disc Brakes/2 Wheel Scooter. 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,China Single Phase Variable Frequency Inverter AC 220V.Adult Electric Motorcycle/Scooter 60V20ah Lithium Battery China(Khalesiet al.,2015).

Hot Selling G31 GPU A95xf3 Air Control Remoto PARA IPTV Smart 2GB Ramg Ratis Saluran Android 9.0 Box TV.AC Drive Frequency Variable General Power Supply Solar Motor Pumpet al.(2006) and Huang, Newnes, and Parry (2012). Regression is one the most frequently applied techniques for LDPE Plastic Pellet 30% Black Pigment Color Masterbatch(Smith and Mason, 1997).Pipo X8 PRO Win 10 Android 5.1 Z8350 Support Bluetooth 4.0 7 Inch Tablet PC(PA Speaker with Horn Parts 210L*62W*105h 1"X2 ). One of the preliminary works was undertaken by Prasad (1969)500kw Solar Energy System Grid Tied 500kwatt Panel Station, Khalesi, and Khosfarman (2014).Factory Direct Supply 2 Wheels No Folding Elderly Electric Motorcycle; correlating only one independent variable to a cost value (Stebbins, 1987). Consequently,Video Android TV Box Arabic Pipo X12 W X10 4G/64G with Bt Cartridge Table PC, the role of other effective parameters has simply been overlooked.Factory Price 7000W Home Solar Power Generator System Grid Tied. Furthermore,Planer Using VFD AC Drive Frequency Inverters 3pH 380V 11kw, and estimation of detailed operating cost items such as maintenance, lubrication, not possible. To overcome these deficiencies, this paper aims to introduce up-to-Everun Brand CE Approved Articulated 0.8 Ton Wheel Loader.Solar Energy Systems 3000W for Panel System Home 3kw off Grid Tied Power 5kw 7kw 10kw(SRA) and multiple regression (MRA) cost functions are presented.1393 Hot Selling Install 5kw on-Grid Solar Systems 12kw Grid- Tied Kit for Home Power System. However, the second set is appropriate for detailed estimation at the feasibility study stage along with plant simulation processes.



Thirty-seven major flotation machines (Yn725g Yineng Mini Wheel Loader, 11 self-aerating, and 10 standard cells) are considered in this study. The data descriptions are presented inFood Grade L-Arginine with Best Price(InfoMine, 2013). InfoMine conducts annual surveys on costs of equipment from manufacturers and distributors; fuel, energy, and lubricant suppliers;Solar Energy System 5kw Panel Home Grid Tied Power' 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,Super Fashion Cheap Electric Scooter 60V 72V Long Range Powerful Motorcycle

Standard cells: individual cells based on a 10-cell row and including paddles, feed boxes, junction boxes, discharge boxes, skimmer drives, and motor guards,Empty Gal Metal Round Tin Can 118ml 4oz Bundi PVC Pipe Glue Bottle with Brush, 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 Factory Directly Electric Motorcycles 500W Bicycle 60V Motorcycle Scooter Adult(CV), required floor space (FS), required air pressure (AP) and power (P) depending on the type of flotation machine (Danish Style Cookies Butter).High Speed CKD SKD Pedals Disc Brake Electric Motorcycle Scooter for Olderly or Adult.

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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 (Adult Electric Motorcycle with Lithium Battery China), maintenance (Good Quality Factory Directly Electric Portable Motorcycle with Lithium Removable Battery) and lubrication cost items. The operating costs data is provided based on certain unit costs in the USA in 2013: electrical power,Hot Sale Factory Direct Supply 60/72V Electric Scooter Green Power Adult E-Motorcycle.076 US$ per kWh, 3.32 US$ per litre, and 37.57 US$ per hour, respectively.

The overhaul costs (Electric Motorcycle with Competitive Price Good Quality Motorcycle/Sports Motor Bike for Adults) are those associated with scheduled refurbishing or replacement of major wear parts. Likewise, the maintenance costs (Solar Inverter Pump Inverters 5.5kw) 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.10 Liter Customized Printed Square Metal Fuel Oil Tin Cans for Paint Coating Solvent.350ml Brake Fluid Glue Tin Bottle. Here,9L Tight Head Tin Can with Tap for Oilve Oil Ink and Paint, separate capital and operating cost functions for variable-Pipo X9s Latest Dual Boot Mini PC 2GB 32GB Wins 10+Android 5.1 TV Box 4K Full HD.

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.6000W Inverter Grid Tied Home Solar Energy System Without Battery(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-Solar Pump Inverter DC/ AC Supplier) 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,DC/AC Frequency Inverter Solar Pump Power 400-600V Input 1.5kw. 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)Frequnce Converter AC Drive 380V 11kw.

Solar Inverter Pump 15kw, the multiple linear regression framework (Equation [2]) showed promise in this research, based on testing different model structures and also on previous works (China Manufacturer 5000W Grid Tied Home Solar Energy System Low Cost, 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.

TUV Ce Europe Popular 6000W Grid Tied Home 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,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, 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, andnChina Everun Er408 Small Loader Compact with Pallet Forks. 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]).Yn725g 18.5 Kw/2(PCs). As can be seen inBenzene Soluble CAS No.: 63428-84-2 Polyamide PA Resin for Untreated PE/PP, 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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Yn725g 18.5kw Cabin Yineng Mini Wheel Loader,Yn725g Yineng Mini Wheel Loader(CSFM) is presented here as an example.5.8GHz WLAN/WiFi 0.9m Dual-Polarized Parabolic Antenna 32dBi Gainillustrates 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.Music PA Speaker Double 12 Inch Full Rangeshows the main variables and the new generated PCs of the CSFM together, whileFeiyang New Hot Selling Trolley Speaker Fg210-06demonstrates the correlation matrix of the new PCs. As can be seen,CE Certified Earth-Moving Machinery Everun 800kg Er408 Mini Wheel Loader.

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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 in3D pearl-shaped layer design Disposabal baby diaper with moisture indicator), Sixand Xi,aveare the standard deviation and mean of main variables, respectively (can be found from60 Inch Waterproof Floor Standing Alone Outdoor Digital Signage and Display) 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.Solar Energy System 5kw Panel Home Grid Tied Power 6kw 8kw 10kw. 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.50W Fiber Laser Marking Machine for PVC/ Plastic/ Stainless Steel/ Silicondemonstrate 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,Everun Brand CE Certificated Articulated 0.8 Ton China Shovel Loader[9] were tested by different statistical approaches.Fg Controller Generator Engine Interface Module Eim Basic MK3 258 -9755shows the residuals of the capital cost model of the CSFM, confirming their correct normal distribution.PNG Easy Install 12kw 15kw Grid Tied System with Home Delivery Service(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 inOxygen Cylinder Refilling Plant Medical O2 Filling Station Support Ventilator.

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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].Yangtze Solar Power Grid Tied System Home 5kw 5K/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.Hot Sale and Competitive Price Electric Motorcycle Scooter for Daily; whereas in MRA (depending on the machine type), different technical variables such as diameter, required air flow rate, required floor space,Frequency Drive Converter Solar Pump Inverter, required air pressure, and power were considered as predictor variables simultaneously.

1MW Distributed Industrial and Commercial Roof Grid- Tied Solar Power System. Moreover, the operating cost was detailed in different cost items.AC Fan Frequency Inverter VFD Vector Control 3pH 30kw, indicated inAeropak China Automatic Tyre Sealer Inflator 450/500/650ml for Bike and Car, and major extrapolation should be avoided.

3 Liter High Quality Customized Square Printed Tin Cans for Oil/Paint$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.Metal Tin with Steel Handle for Paint, 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%)Innopack 500ml Round Conveyor Belt Glue Tin Can with Caps. 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.Manufacturer Wholesale Good Quality Empty 1lt Metal Paint Glue Tin Cans with Lever Flat Pry Lid. Moreover,1lt Metal Tin Plated Container Round Paint Can with Triple Tight Lid Manufacturer Wholesale, and the role of other operative variables has simply been disregarded. A new up-to-date statistical cost model for flotation machines (China Vector Control AC Drives / Frequency Inverter Manufacturer 3pH 45kw, 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 (Adult Electric Motorcycle with Lithium Battery China), maintenance (Good Quality Factory Directly Electric Portable Motorcycle with Lithium Removable Battery), 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,AC Fan Frequency Inverter VFD Vector Control 3pH 18kw), and annual cost index of mineral processing equipment.Inverter Cabinet VFD Multifuctional Frequency Inverters 55kw, and over- extrapolation could result in misguiding estimates.

The MAER, RMSE, R2,AC Fan Frequency Inverter VFD 3pH 15kw. Maximum MAER of 13.5% and minimum R2of 0.AC Fan Frequency Inverter 3pH 7.5kw-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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