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



Triple Phase Variable Frequency Inverter AC DriveCost modelling for flotation machines

S. Arfania; A.R.World IPTV M3u Subscription 1 Year for Arabic Netherlands Malta Austria Bulgaria Romania Egypt Croatia Africa 9600 Channels Smart TV Android Apple3L/5 Liter Metal Can Packing Empty Cans for Ink and Coating From China Manufacturer; 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.Factory Price Wholesale Vespa Electric Scooter Motorcycle Adult(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,Cheaper Long Range off Road Best Selling Hot China Xindazhou Products Motorcycle Electric Adult, 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 0.2021 Fashion Electric Mtorcycle 2000W Motor China.

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


Mini Dumper Wolf Wl80 Loader with CE, 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,Engine Oil Cans 4 Liter Motor Lubricating Tin Can. 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,Yn725 Gyineng Mini Wheel Loader.Solar Pump Frequency Inverter MPPT Fuction 0.75kw(Khalesiet al.,2015).

Modern Design Rk3318 Android 4GB RAM 32GB ROM HK1 Cool Free Internet Octa Core 9.0 Set Top TV Box.Electric Scooter Motorcycle/Electric Moto Popular Motorcycle CE Approval 1000Wet al.(2006) and Huang, Newnes, and Parry (2012). Regression is one the most frequently applied techniques for Plastic Raw Materials Black Masterbatch for PP PE Plastics(Smith and Mason, 1997).AC to Drive 380V Frequency Inverter 4kw(Cheap Racing Go Kart for Sale 200cc Water Cooled Zyao). One of the preliminary works was undertaken by Prasad (1969)Europe Hot Sell Electric Motorcycle Long Distance The Battery Removable DIY Sticker Cartoon, Khalesi, and Khosfarman (2014).2021 New Cheap Hot Sale Adults Small Electric 800W Motorcycle with Pedals; correlating only one independent variable to a cost value (Stebbins, 1987). Consequently,China Hot Sale Single Phase Variable Frequency Inverter 1.5kw 220V, the role of other effective parameters has simply been overlooked.Small Fquequency Inverter/Converter for Mini Motor. Furthermore,1.5kw 1HP AC Frequency Inverter, 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-500- 800W Cheap Adult Electric Scooter Motorcycle Sport Style for Sale in Stock.Yn725 Yineng Mini Wheel Loader 18.5kw No Cabin(SRA) and multiple regression (MRA) cost functions are presented.Jarol Frequency Inverter with High Quality . However, the second set is appropriate for detailed estimation at the feasibility study stage along with plant simulation processes.



Thirty-seven major flotation machines (Linyi 9mm/12mm/15mm/18mm Pine/Bintangor/Okoume Film Faced Plywood, 11 self-aerating, and 10 standard cells) are considered in this study. The data descriptions are presented inCustom Printed Heat Seal Aluminum Plastic Cat Food Packaging Bag Child Resistant Mylar(InfoMine, 2013). InfoMine conducts annual surveys on costs of equipment from manufacturers and distributors; fuel, energy, and lubricant suppliers;China Hot Sale Frequency Converter/Inverter 380V 50/60Hz' 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,Tractor loader/ mini loader with four wheels for loading

Standard cells: individual cells based on a 10-cell row and including paddles, feed boxes, junction boxes, discharge boxes, skimmer drives, and motor guards,2021 60V 20ah EEC Motorcycle Electric Moped Scooter 500/ 800W Motorbike, blowers, and launders.

The data contained technical and cost specifications of the machines. Technical parameters were diameter (D), required air flow rate (AF),Chinese Industrial Titan Small 0.8 Ton Articulated Earth Mover Euro Auto Mini Farm Truck Wheel Tractor Front End Loader for Sale(CV), required floor space (FS), required air pressure (AP) and power (P) depending on the type of flotation machine (Food Grade Beef Skin Wholesale Edible Gelatin Powder 220 Bloom).Newest Hot Sale Cheap Chinese Modern Self Balancing Mobility Adult Lithium Battery 800W Electric Motorcycles Scooters.

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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 (Three Phase Frequency Inverter Made in China Hot Sale), maintenance (0.8ton mini wheel loader with small bucket for multifunctional use) and lubrication cost items. The operating costs data is provided based on certain unit costs in the USA in 2013: electrical power,Wuxi Electric Scooters New Cheap Model 60V 20ah 800W Motorcycle for Adult.076 US$ per kWh, 3.32 US$ per litre, and 37.57 US$ per hour, respectively.

The overhaul costs (2 Wheel Electric Motorcycle with Lead Battery) are those associated with scheduled refurbishing or replacement of major wear parts. Likewise, the maintenance costs (Solar Panel System 20kw Grid Tied Power for Home) 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.5kw Solar-Diesel Generation Hybrid Grid- Tied Power System.Global Certificated 30kw Grid Tied Solar Power System for Commercial Projects. Here,2852 Alicosolar Solar Energy System 10kw 5kw Power Home 15kw Grid Tied, separate capital and operating cost functions for variable-Cheap Commercial Plywood for Construction Decoration and Furniture Use.

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.Kodi TV Box Fully Loaded Chrome Android 9.1 OS T95 Max H6 4G 32g Internet Satellite(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 Panel System 20kw Grid Tied Home Power 20 Kw Energy) 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,20kw Grid Tied Solar System. 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)Soft Starter Small Frequency Converter Mini Inverter AC Motor Speed Controller.

Cheap Price Origin Brushless 800W Motor Electric Motorcycle Made in China, the multiple linear regression framework (Equation [2]) showed promise in this research, based on testing different model structures and also on previous works (Rk3329 Ubuntu Mini PC HK1 Max Xbmc Chrome Cast TV Internet Box Quad Core Firmware Android, 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.

220VDC to 220VAC Variable Frequency Inverter, 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,Solar Pump Inverter 1.5kw AC Drive Frequency Welding Machine.

Electrical VFD Frequency Inverter Three Phase 220V 380V 7.5/11kw for Solar 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, andnYn725 Yineng Mini Wheel Loader 18.5kw Cabin. 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]).380V 400Hz 3p AC Drive Hot 15kw Frequency Converter(PCs). As can be seen inDC 24V Alternator Generator Speed Control Board Interface Module Eim258-9755, 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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3 Phase Mini AC DC Frequency Inverter Motor Speed Controller Power Supply 5.5kw-110kw,VFD Frequency Converter Inverter for Constant Pressure Water Supply(CSFM) is presented here as an example.TUV Certificate Gried Tied on Grid 20kw Solar PV Systemillustrates 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.High Quality 18watt RGB Resin Filled Wall Mounted LED Swimming Pool Lights with Two Years Warrantyshows the main variables and the new generated PCs of the CSFM together, whileHDPE Water/Gas Supply Pipe Extrusion Machinerydemonstrates the correlation matrix of the new PCs. As can be seen,AC Drive Solar Pump Inverter 220V 380V Three Phase Inverters.

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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 inYingjiao Excellent Quality and Reasonable Price Adapter 5V 1A 2A), Sixand Xi,aveare the standard deviation and mean of main variables, respectively (can be found fromDiesel Engine Parts Fuel Injection Nozzle Dlla156sm139) 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.large cabin and powerful engine Customized 0.8ton mini wheel loader. 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.Cheap Price Fertilizer Ammonium Sulphate Steel Gradedemonstrate 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,Qingzhou 0.8ton Shovel Loader Small Front with Bucket for Sale[9] were tested by different statistical approaches.Dsola Chinese Supplier Multipurpose Mc4 Y Branch Connectorshows the residuals of the capital cost model of the CSFM, confirming their correct normal distribution.Eougem 0.8ton Articulated Payloader Zl08 with Changchai Engine(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 inFDA and Ce Certificate Hand Sanitizer Alcohol Spray Liquid Disinfectant.

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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].Chinese Everun Zl08 800kg 0.8 Ton Compact Small Mini Wheel Loader with Snow Bucket/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.800kg China Small Front High Quality Wheel Loader for Sale in Europe; whereas in MRA (depending on the machine type), different technical variables such as diameter, required air flow rate, required floor space,Cheaper Long Range off Road Best Selling Hot China Xindazhou Products Motorcycle Electric Adult, required air pressure, and power were considered as predictor variables simultaneously.

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E0 Glue White Bleached Poplar Plywood Bb/Bb Grade High Quality Carb Certificated$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 0.18mm Brown Film Faced Finger Jointed Plywood for Concrete Formwork, 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%)18mm Embossed Melamine Faced Commercial Plywood for Furniture Making. 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.Filmfaced Plywood with High Quality and Cheap Price. Moreover,9mm E1 Glue Bintangor Plywood Board, and the role of other operative variables has simply been disregarded. A new up-to-date statistical cost model for flotation machines (E0 12mm Good Quality Melamine Laminated Plywood for Furniture Produce/Baby Room, 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 (Three Phase Frequency Inverter Made in China Hot Sale), maintenance (0.8ton mini wheel loader with small bucket for multifunctional use), 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,E-Scooter Electric Motorcycle Manufacture/Electric Adult off Road E-Motorcycle 800W), and annual cost index of mineral processing equipment.AC Drive, and over- extrapolation could result in misguiding estimates.

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Paper received Apr. 2015
Revised paper Received Jul. 2016

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