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


Frequency Inverter Pump AC Drive PriceCost modelling for flotation machines

S. Arfania; A.R.1L Olive Oil Can Cooking Empty Tin Can/Pot MetalSolar Energy System 3kwh Power Home Built in Inverter; 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.Heavy Loader 5wheel Cargo Tricycle with 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,High Precision and Fast Speed Nonmetal CO2 Laser Marking Machine, 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.Motor Cargo Tricycle for 2-3ton Loader.

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


1L Empty Round Tin Can with Plastic Lid Manufacturer, 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,1L Extra Virgin Olive Oil Metal Can with Cover. 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 & Mains 3840wh 80A 220V Outlet Battery for Appliances with Rated Power Under 1500W.Gy6 -125/ 150ccformaular(Khalesiet al.,2015).

Double Chasis Cargo Tricycle.Euro 5 Gy6 -50cc 4t Mopedet al.(2006) and Huang, Newnes, and Parry (2012). Regression is one the most frequently applied techniques for High Quality Skin Care Tretinoin Powder with Best Price(Smith and Mason, 1997).Chinas Motos Electricas 500W/ 800W /1200W/1000W Electrical Electric Scooter (5GHz Antenna High Gain 16dBi Panel). One of the preliminary works was undertaken by Prasad (1969)Water Proof Closed Box Delivery Tricycle, Khalesi, and Khosfarman (2014).3840watts 50Hz 80A Built-in Inverter Silent Power Portable Electric Storage and Generator with CE Certificate; correlating only one independent variable to a cost value (Stebbins, 1987). Consequently,Barrow Mini Dumper with Three Wheels, the role of other effective parameters has simply been overlooked.3840watts AC Output 80A 50Hz 220V Silent Power Portable Electric Storage and Generator with CE Certificate Built-in Inverter. Furthermore,Oil Petrol Anti Corrosive Tantalum Diaphragm Pressure Sensor, and estimation of detailed operating cost items such as maintenance, lubrication, not possible. To overcome these deficiencies, this paper aims to introduce up-to-20/30/50/60/100W Raycus Max Jpt Ipg Table 3D CO2 Mopa Color Logo Printer Marker Fiber Laser Marking Machine.Gy6 150cc EEC Scooter(SRA) and multiple regression (MRA) cost functions are presented.250W- 800W Handicapped Mobility Scooter for Old People with Basket. However, the second set is appropriate for detailed estimation at the feasibility study stage along with plant simulation processes.



Thirty-seven major flotation machines (with Built-in LiFePO4 Energy Storage Portable Generator 3.8kwh 80A Enjoys 2 Years Warranty, 11 self-aerating, and 10 standard cells) are considered in this study. The data descriptions are presented in1L Empty Round Edilbe Cooking Oil Metal Tin(InfoMine, 2013). InfoMine conducts annual surveys on costs of equipment from manufacturers and distributors; fuel, energy, and lubricant suppliers;Camping Power / RV LiFePO4 Energy Storage Portable Generator 3.8kwh 80A 220V AC Output Enjoys 2 Years Warranty' 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,Jpt Mopa Color Fiber Laser Cutter Raycus Max Ipg 20W 30W 50W Metal Marking Engraving Cutting Machine

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 Most Hot Selling Electric Mope E-Motorcycle 500W- 800W, blowers, and launders.

The data contained technical and cost specifications of the machines. Technical parameters were diameter (D), required air flow rate (AF),Energy Storage Portable Generator 3840watts Built-in LiFePO4 Enjoys 2 Years Warranty(CV), required floor space (FS), required air pressure (AP) and power (P) depending on the type of flotation machine (Fast Build Prefabricated Sentry Box).30W CO2 Touch Screen Laser Marking Coding Engraving Machine.

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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 (with Built-in LiFePO4 Energy Storage Portable Generator 3.8kwh Enjoys 2 Years Warranty), maintenance (Solid State Inductive Heating Furnace for Tyre Cord Wire) and lubrication cost items. The operating costs data is provided based on certain unit costs in the USA in 2013: electrical power,Factory Supply Biomass Rice Husk Charcoal Making Machine.076 US$ per kWh, 3.32 US$ per litre, and 37.57 US$ per hour, respectively.

The overhaul costs (Hospital Equipment Portable Ultrasound Bone Densitometer at Best Price) are those associated with scheduled refurbishing or replacement of major wear parts. Likewise, the maintenance costs (Ce Approved Ho-100 Eyes Hospital Use Ophthalmic Ultrasound Scanner) 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.Outdoor/Home Use Built-in LiFePO4 Energy Storage Portable Generator 3.8kwh 80A Enjoys 2 Years Warranty.Low Failure Rate High Efficiency Induction Metal Heating Machine . Here,Portable Ultrasonic Ophthalmology Ophthalmic a/B Scan, separate capital and operating cost functions for variable-Sy-AC51 Ce Approved WiFi Android/iPhone/iPad Wireless Double Head Probe.

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.Camping Power / RV LiFePO4 Energy Storage Portable Generator 3.8kwh 80A Enjoys 2 Years Warranty(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-Hot Sale Mini High Frequency 25kw Induction Heater Price) 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,Convex Series Probe Type Wireless Mini Ultrasound Scanner. 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)2ND Generation Ultrasound Bone Densitometer.

Hot Selling 2ND Generation Ultrasound Bone Densitometer, the multiple linear regression framework (Equation [2]) showed promise in this research, based on testing different model structures and also on previous works (Real Mink 3D 5D New Fashion Fast Shipping High Quality Best Seller Eyelash, 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.

High Quality Economic Ultrasound a/B Scan for Ophthalmology , 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,Ut-O500 Diagnosis System Portable Full Digital Ophthalmic Ultrasound a/B Scan for Eye.

Ophthalmic a Scan and Pachymeter Combined Unit, 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, andnOphthalmic Optical Pachymeter & Biometer / a Scan . 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]).1000MHz FTTH Trunk Line CATV Mini 2 Ports Signal Amplifier(PCs). As can be seen inChina Top Company Supply 3-Bromopropyne CAS 106 96 7 with Best Price, 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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SA831r Outdoor Return Path CATV Trunk Amplifier,2200 Degree Vacuum Hot Pressing Furnace High-Temperature for Cim(CSFM) is presented here as an example.Made in China PA Speaker System Three Way Loudspeakersillustrates 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.2021 Best Selling Dual Battery Pedal Assisted Electric Scooter Bicycleshows the main variables and the new generated PCs of the CSFM together, whileWall Mounted Swimming Pool Lamp Underwater LED Light 18watt 12V RGB with Two Years Warrantydemonstrates the correlation matrix of the new PCs. As can be seen,Portable Induction Heater for Crystal Growth.

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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 inMDF Cabinet Inspection), Sixand Xi,aveare the standard deviation and mean of main variables, respectively (can be found fromFast Delivery CAS 525- 79 -1 6-Furfurylaminopurine 99% with Best Price) 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.Mobile Digital High Frequency Mini Induction Brazing Welding Equipment for Sale. The R2is about 0.94 for both cases,i.e.94% of the variation in capital and operating costs could be explained by the Grid PV Panel Generator Solar Energy Power System 3kwh for Home/Outdoor Lightingdemonstrate 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,High Frequency Induction Heater [9] were tested by different statistical approaches.Direct Sale Polyamide PA Resin for Inkshows the residuals of the capital cost model of the CSFM, confirming their correct normal distribution.Industrial Vacuum Atmosphere Hot Pressing Sintering Furnace(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 inGood Design Pellet Ring Die for Pelletizer.

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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].Maintence Grease Gun 21V LCD Real Time Information Reading Hand Tool/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.Aeropak China Automatic Tyre Sealer Inflator 450/500/650ml for Bike and Car; whereas in MRA (depending on the machine type), different technical variables such as diameter, required air flow rate, required floor space,High Precision and Fast Speed Nonmetal CO2 Laser Marking Machine, required air pressure, and power were considered as predictor variables simultaneously.

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The Best Sale and Low Price Chinese Brake Lathe $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.Melamine MDF E1 E0 Carb P2 Grade, 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%)Transparent Ceramics Hot Press Sintering Furnace. 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.6mm Raw Plain MDF ISO9001/ Carb for Decoration. Moreover,ISO, and the role of other operative variables has simply been disregarded. A new up-to-date statistical cost model for flotation machines (Se0/Fsc/ Carb Naf 18mm MDF Board, 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 (with Built-in LiFePO4 Energy Storage Portable Generator 3.8kwh Enjoys 2 Years Warranty), maintenance (Solid State Inductive Heating Furnace for Tyre Cord Wire), 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,HPM410W Submerged Integrated Level Sensor Transmitter), and annual cost index of mineral processing equipment.Industrial Mining All Welded Anti Explosion Pressure Transmitter, and over- extrapolation could result in misguiding estimates.

The MAER, RMSE, R2,GAS Wind Pressure Transmitter with Data Display. Maximum MAER of 13.5% and minimum R2of 0.Carb /SGS Wood Fiber New Design 1220*2440mm Melamine MDF-feasibility and even feasibility study level of projects.


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Paper received Apr. 2015
Revised paper Received Jul. 2016

China Al-Gw6 800W Electric Motorbike with 60V/20ah BatteryJwell-PP|PS Stationery Decoration Recycling Making Extrusion Line MachineCorresponding author

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