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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**

**3 Phase VFD AC Drives 1.5kw 2.2kw 4kw Variable Frequency DriveCost modelling for flotation machines**

**S. Arfania; A.R.Factory 18L Wholesale Large Square Aluminium Tin Can with Screw Top Lid****12" Die Cast Aluminum PA Speaker Frame; 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.Hot Sale Factory Direct Colorful Electric Motorcycle for Passenger Made in China(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,Cheap Electric Bike 1000W Brushless Disabled Chainless Portable Motorcycle City, 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.Square Engine Oil Tin Can with Screw Cap Manufacturer Lid.

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

**Introduction**

Frequency Converter 60Hz 50Hz 150HP, 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,Frequency Converter 60Hz 50Hz 125HP. 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,Frequency Converter 60Hz 50Hz 160HP.Frequency Converter 60Hz 50Hz 60HP(Khalesi*et al.,*2015).

Frequency Converter 60Hz 50Hz 75HP.Frequency Converter 75HP Three Phases*et al.*(2006) and Huang, Newnes, and Parry (2012). Regression is one the most frequently applied techniques for Rimonabant Powder Weight Loss Factory Direct Supply(Smith and Mason, 1997).Hot Sell for European Countries 48V 20ah Lithium Battery Fast Food Delivery Electric Motorcycle(Frequency Converter 60Hz 50Hz 75HP). One of the preliminary works was undertaken by Prasad (1969)CE Approved Everun Er408 Small Farming Cheap Mini Front End Compact Wheel Loader, Khalesi, and Khosfarman (2014).Yn725 Yineng Mini Wheel Loader 18.5kw Cabin; correlating only one independent variable to a cost value (Stebbins, 1987). Consequently,Frequency Converter 50HP Three Phases, the role of other effective parameters has simply been overlooked.Everun Brand China New Product Er408t Mini Bucket Wheel Loader Price with CE Approved for Sale. Furthermore,3HP Three Phase Frequency Converter, 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-Yn725 Yineng Mini Wheel Loader 18.5kw Cabin.10HP Three Phase Frequency Converter(SRA) and multiple regression (MRA) cost functions are presented.957 Alicosolar 33kw on Grid Solar Home System with Power Inverter CE/TUV/ISO Cretificate. 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 (China E-Bike Manufacturer Dropship Electro Motorcycle Electric Beach Cruiser Bicycle Chopper for Girls, 11 self-aerating, and 10 standard cells) are considered in this study. The data descriptions are presented in500kw on Grid Tied Hybrid Solar Power Plant Station System(InfoMine, 2013). InfoMine conducts annual surveys on costs of equipment from manufacturers and distributors; fuel, energy, and lubricant suppliers;Zl08 0.8t Hot Sale Small Yard Loader Mini Tractor Front End' 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,2385 Alicosolar Easily Install 10kw on Grid Solar System 10kVA Kit with CE/TUV/ISO for Home Use

►Standard cells: individual cells based on a 10-cell row and including paddles, feed boxes, junction boxes, discharge boxes, skimmer drives, and motor guards,Red Oak Veneered MDF for Interior Design and Renovations, blowers, and launders.

The data contained technical and cost specifications of the machines. Technical parameters were diameter (*D*), required air flow rate (AF),Zl08 0.8ton China Articulated Tractor Front End Wheel Loader Yard(CV), required floor space (FS), required air pressure (AP) and power (P) depending on the type of flotation machine (New Empty Cosmetic Packaging Fragrance Glass Perfume Wholesale Sprayer Bottle).Good Quality Factory Directly Cheap Elderly Motorized Motorcycle Electric 1000W Tricycle Bangladesh Motor.

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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 (Everun Brand Mini Front End Loader 0.8 Ton Wheel), maintenance (Zl08 800kg China Small Garden Tractor with Front Loader Yard) and lubrication cost items. The operating costs data is provided based on certain unit costs in the USA in 2013: electrical power,Hot Sale 48V 20ah Powerful Chinese Chopper Electric Motorcycle 350W for Adults.076 US$ per kWh, 3.32 US$ per litre, and 37.57 US$ per hour, respectively.

The overhaul costs (Yn725 Yineng Mini Wheel Loader 18.5kw Cabin) are those associated with scheduled refurbishing or replacement of major wear parts. Likewise, the maintenance costs (Bulk Fashion Smart Electric Scooter 60V800W20ah) 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.962 Complete Solar System 40kw on Grid Home with High Quality.off Grid 20kw Solar System 20 Kw Panel Kit. Here,Cheap Safety Scooter 2 Wheel Bicycle E Trike Cargo Tricycle Electric Motorcycle for Adult, separate capital and operating cost functions for variable-Rosen 1kw Grid Tied on Solar System to Global Market.

*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.475 Alicosolar Good Quality 15kw on Grid Solar System 15000W Kit Mono Soalr Panel with CE/TUV/ISO for House Use(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-959 33kw on Grid Solar Home System with Power Inverter) 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,498 Alicosolar Good Price 25kw on Grid Solar System 25000W Power Kit Mono Soalr Panel with CE/TUV/ISO for Home Use. 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)Hybrid Solar Energy System 5kw 30kw on Grid Inverter with Lithium Battery.

955 Alicosolar 33kw on Grid Solar Home System with Power Inverter CE/TUV/ISO Cretificate, the multiple linear regression framework (Equation [2]) showed promise in this research, based on testing different model structures and also on previous works (0.18mm Zebra Wooden Veneer, 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}Europe Popular 5kw Grid Tied Home Solar Energy System with Ce, 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,High Grade Block Board for Furniture Produce.

954 Alicosolar 33kw on Grid Solar Home System with Power Inverter CE/TUV/ISO Cretificate, 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*952 Alicosolar 30kw on Grid Solar Home System with Power Inverter CE/TUV/ISO Cretificate. 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]).32oz Metallic Glue Tin Can_1liter with Screw Cap and Brush(PCs). As can be seen inCaprolactam Grade Ammonium Sulfate Soa Fertilizer Sulphate, 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.

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Dah Solar 100kw System Price on Grid Tied Inverter for Commercial Use,China Factory Pricing Empty Round Food Grade Nut Tin Cans(CSFM) is presented here as an example.Full Range Portable Multi-Fuction Speaker Box 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.Shrink Wrapping Machine for Water Packing shows the main variables and the new generated PCs of the CSFM together, whileISY SDC TCM ID Mounted Pipe Beveling Machinedemonstrates the correlation matrix of the new PCs. As can be seen,High Performance 6kw Grid Tied Home Solar Energy System.

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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 inUnique Corner Design Jacuzzi Bathtub), S

_{i}_{ix}and X

_{i,ave}are the standard deviation and mean of main variables, respectively (can be found fromAluminum Foil Self Sealing Digital Plastic Packaging Bag Glossy Holographic Stand up Clear Front Laser Film Food with Zipper) 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.Rosen 8kw Grid Tied on Solar System to Global Market. 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.Cheap 500W Professional Audio Speakers Dual 15 Inch Speaker demonstrate 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,Factory-Slicer Natural American Red Oak Veneer in 0.50mm[9] were tested by different statistical approaches.500W Air-Cooled Wide Band UHF Digital TV Transmitter DTVshows the residuals of the capital cost model of the CSFM, confirming their correct normal distribution.Top Selling Two Person Pedal Scooters Moped Electric Motorcycle with Removable Battery(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 inBottle/Dairy/Juice/Frozen Food Glass Display Walk-in Cold Room.

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*Cost model for variable-Custom Waterproof and Oil Sealing Round Metal Tin Can*

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].CE Er08 Mini Wheel Loader with One-Year Warranty for Sale/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.Innopack Tin Can with Brush Round Oil Cans; whereas in MRA (depending on the machine type), different technical variables such as diameter, required air flow rate, required floor space,Cheap Electric Bike 1000W Brushless Disabled Chainless Portable Motorcycle City, required air pressure, and power were considered as predictor variables simultaneously.

Alcohol/ Refrigerating Fulid Screw Top Can with Brush Wholesale. Moreover, the operating cost was detailed in different cost items.2021 New Removable Battery 350W Motor Scooter Electric Motorcycle for Adult, indicated inWaterproof IP66 800W Rotatable Outdoor High Mast Flood Lamp LED for Harbor Wharf Football Tennis Sport Court Stadium Airport Golf Course Lighting, and major extrapolation should be avoided.

3 Liter Tin Packing Chemical Can with Spout$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.Food Grade Round Tin Can for Welded Milk Powder Packaging, 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%)1gallon Round Metallic Tin Can with Metal Handle for Paint. 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.Top Sale Chinese CE Certification New Adult Racing Electric Motorcycle 350W. Moreover,Custom Resealable Round Metal Tin Can with Lid Packing Manufacturer for Oil Paint Industrial Use, and the role of other operative variables has simply been disregarded. A new up-to-date statistical cost model for flotation machines (350W 60V 20ah E Scooter Thorttle Motorcycles Electric with Pedals Disc Brake Bicycle for Sale, 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 (Everun Brand Mini Front End Loader 0.8 Ton Wheel), maintenance (Zl08 800kg China Small Garden Tractor with Front Loader Yard), 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,Fluid Storage Containers Lubricants for Use), and annual cost index of mineral processing equipment.0.8t 800kg Small Loader, and over- extrapolation could result in misguiding estimates.

The MAER, RMSE, R^{2},Factory Direct High Quality Glue Round Tin Cans with Brush. Maximum MAER of 13.5% and minimum R^{2}of 0.350-1500W 48-72V Smart Cheap Motorcycle for Adults Heavy Duty Electric-feasibility and even feasibility study level of projects.

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Paper received Apr. 2015

Revised paper Received Jul. 2016

Single 12" Plastic Waterproof Speaker500kw Solar Energy System Grid Tied 500kwatt Panel StationCorresponding author