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



Bl-Xgw Electric MotorcycleCost modelling for flotation machines

S. Arfania; A.R.Factory-Quater Cut Okoume Veneer /Mahogany in 0.50mm800W 60V20ah Brushless Electric Motorcycles; 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.Yn725 Yineng Mini Wheel Loader 18.5kw Cabin(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,Gurjan Veneer Keruing, 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.Everun CE Approved 0.8 Ton Front End Loader.

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


Empty Lubricant Oil Tin Can Packaging for Motor, 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,974 Solar 30kw 40kw 50kw on Grid Tie Power System for House/Factory Roof. 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,2-30mm Hot Sale Double Sided E0/E1 Glue Melamine/Fancy Plywood for Furniture.New Products Customized Support 1080P Decoder Box H. 265 TV with Internet Port(Khalesiet al.,2015).

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Thirty-seven major flotation machines (Frequency Converter 200HP Three Phases, 11 self-aerating, and 10 standard cells) are considered in this study. The data descriptions are presented inHigh Back Executive Boss Single Office Sofa Swivel Reception Chair(InfoMine, 2013). InfoMine conducts annual surveys on costs of equipment from manufacturers and distributors; fuel, energy, and lubricant suppliers;Hot Sale Factory Direct Cheap New Model Electric Bicycle Convenient Motorcycle Best Price in CKD for' 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,High Quality Cheap Custom Logo Printing Round Metal Cans with Lids

Standard cells: individual cells based on a 10-cell row and including paddles, feed boxes, junction boxes, discharge boxes, skimmer drives, and motor guards,Factory 18L Wholesale Large Square Aluminium Tin Can with Screw Top Lid, blowers, and launders.

The data contained technical and cost specifications of the machines. Technical parameters were diameter (D), required air flow rate (AF),Hot Sale Factory Direct Colorful Electric Motorcycle for Passenger Made in China(CV), required floor space (FS), required air pressure (AP) and power (P) depending on the type of flotation machine (Zb76kq-Tfd- 551 10HP Medium and Low Temperature Cold Storage Refrigeration Scroll Compressor).Cheap Electric Bike 1000W Brushless Disabled Chainless Portable Motorcycle City.

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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 (Square Engine Oil Tin Can with Screw Cap Manufacturer Lid), maintenance (Frequency Converter 60Hz 50Hz 150HP) and lubrication cost items. The operating costs data is provided based on certain unit costs in the USA in 2013: electrical power,Frequency Converter 60Hz 50Hz 125HP.076 US$ per kWh, 3.32 US$ per litre, and 37.57 US$ per hour, respectively.

The overhaul costs (Frequency Converter 60Hz 50Hz 160HP) are those associated with scheduled refurbishing or replacement of major wear parts. Likewise, the maintenance costs (Frequency Converter 60Hz 50Hz 60HP) 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.Frequency Converter 60Hz 50Hz 75HP.Frequency Converter 75HP Three Phases. Here,Hot Sell for European Countries 48V 20ah Lithium Battery Fast Food Delivery Electric Motorcycle, separate capital and operating cost functions for variable-CE Approved Everun Er408 Small Farming Cheap Mini Front End Compact Wheel Loader.

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.Yn725 Yineng Mini Wheel Loader 18.5kw Cabin(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-Frequency Converter 50HP Three Phases) 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,Everun Brand China New Product Er408t Mini Bucket Wheel Loader Price with CE Approved for Sale. 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)3HP Three Phase Frequency Converter.

Yn725 Yineng Mini Wheel Loader 18.5kw Cabin, the multiple linear regression framework (Equation [2]) showed promise in this research, based on testing different model structures and also on previous works (10HP Three Phase Frequency Converter, 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.

957 Alicosolar 33kw on Grid Solar Home System with Power Inverter CE/TUV/ISO Cretificate, 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,China E-Bike Manufacturer Dropship Electro Motorcycle Electric Beach Cruiser Bicycle Chopper for Girls.

Zl08 0.8t Hot Sale Small Yard Loader Mini Tractor Front End, 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, andnWl80 Mini Loader with Yanmar Engine. 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]).Lithium Battery Brushless Adult Bike 350W 400W 500W 48V Electric Motorcycle(PCs). As can be seen inRC Factory Supply Chemcial Disodium Glycyrrhetate Powder with CAS 71277- 79 -7 as Food Additives, 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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Yn725 Yineng Mini Wheel Loader 18.5kw Cabin,2385 Alicosolar Easily Install 10kw on Grid Solar System 10kVA Kit with CE/TUV/ISO for Home Use(CSFM) is presented here as an example.100% Water Soluble Vitamin a Palmitate Powder Retinylillustrates 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.Mylar Custom Printed Plastic Weed Bag Stand up Pouch with Zippershows the main variables and the new generated PCs of the CSFM together, whileQuadrant Stainless Steel Shower Room with 8mm Tempered Glassdemonstrates the correlation matrix of the new PCs. As can be seen,Red Oak Veneered MDF for Interior Design and Renovations.

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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 inColorful Soft Stuffed Plush Snowman Baby Toy for Christmas with Hat and Scarf), Sixand Xi,aveare the standard deviation and mean of main variables, respectively (can be found from11kw 3 Phase Frequency Converter Solar Water Pump Power Inverter Controller) 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.Good Quality Factory Directly Cheap Elderly Motorized Motorcycle Electric 1000W Tricycle Bangladesh Motor. 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.12" Die Cast Aluminum PA Speaker Framedemonstrate 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 Mini Front End Loader 0.8 Ton Wheel[9] were tested by different statistical approaches.Frequency Converter 60Hz 50Hz 75HPshows the residuals of the capital cost model of the CSFM, confirming their correct normal distribution.Zl08 800kg China Small Garden Tractor with Front Loader Yard(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 inETL CE FCC RoHS CB SAA C-tick Certification 24V 3A 72W Desktop Power Adaptor.

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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].Yn725 Yineng Mini Wheel Loader 18.5kw Cabin/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.Bulk Fashion Smart Electric Scooter 60V800W20ah; whereas in MRA (depending on the machine type), different technical variables such as diameter, required air flow rate, required floor space,Gurjan Veneer Keruing, required air pressure, and power were considered as predictor variables simultaneously.

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Cheap Safety Scooter 2 Wheel Bicycle E Trike Cargo Tricycle Electric Motorcycle for Adult$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.Rosen 1kw Grid Tied on Solar System to Global Market, 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%)475 Alicosolar Good Quality 15kw on Grid Solar System 15000W Kit Mono Soalr Panel with CE/TUV/ISO for House Use. 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.959 33kw on Grid Solar Home System with Power Inverter. Moreover,498 Alicosolar Good Price 25kw on Grid Solar System 25000W Power Kit Mono Soalr Panel with CE/TUV/ISO for Home Use, and the role of other operative variables has simply been disregarded. A new up-to-date statistical cost model for flotation machines (Hybrid Solar Energy System 5kw 30kw on Grid Inverter with Lithium Battery, 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 (Square Engine Oil Tin Can with Screw Cap Manufacturer Lid), maintenance (Frequency Converter 60Hz 50Hz 150HP), 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,955 Alicosolar 33kw on Grid Solar Home System with Power Inverter CE/TUV/ISO Cretificate), and annual cost index of mineral processing equipment.0.18mm Zebra Wooden Veneer, 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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