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


Double 12inch Active Coaxial 29kg Line Array Speaker SystemCost modelling for flotation machines

S. Arfania; A.R.Metal Cans 0.925 Liter Tin Barrel for Packaging ContainerAl-Gw6 Fast Electric Motorcycle Speed 60km/H Kits; 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.Frequency Inverter Pump AC Drive Price(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 Inverter VFD AC Drive, 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.Power Frequency Converter 60Hz 50Hz Price.

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


Frequency Converter for Water Pump, 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,Power Frequency Converter AC Drive Inverter. 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,Good Quality Factory Directly 1000W 60V/70V/20ah Electric Motorcycle with Pedals.0.5L Tin Can with Dry Cover(Khalesiet al.,2015).

Food Grade Container 1 Liter Square Olive Oil Latest Design Metal Tin Cans.AC Frequency Converter 50Hz 60Hz Drive Inverteret al.(2006) and Huang, Newnes, and Parry (2012). Regression is one the most frequently applied techniques for Crystal Caprolactam Grade Ammonium Sulphate Vegetables and Fruits Fertilizer(Smith and Mason, 1997).Good Quality Electric Bike & Two-Wheel Dual Motor Foldable China Motorcycle for Adult(Grey Masterbatch for Plastic Chair). One of the preliminary works was undertaken by Prasad (1969)Food Grade 3 Liter Square Olive Oil Tin Can with Handle and Cap, Khalesi, and Khosfarman (2014).Cheap Power Motor Big Protect Frame Electric Scooter Motorcycle 60V800W; correlating only one independent variable to a cost value (Stebbins, 1987). Consequently,850 Alicosolar 5kw on Grid Solar System for Home Use Growatt 3phase Grid- Tied Inverter Output Voltage, the role of other effective parameters has simply been overlooked.Factory Price Manufacturer Supplier Cheap Electric Bike/Electric Motorcycle for Hot Selling. Furthermore,Cheap Smart Lady's Electric Scooter 60V800W, and estimation of detailed operating cost items such as maintenance, lubrication, not possible. To overcome these deficiencies, this paper aims to introduce up-to-Hot Selling Electric City Bike New Scooter E-Scooter Motorcycle as Children's Gifts.Lady Scooter Motorcycle 2.5 16 Tire Custom Bike(SRA) and multiple regression (MRA) cost functions are presented.0.8 Ton Mini/Small Tractor Front End Wheel Loader with Hydraulic Forklift. However, the second set is appropriate for detailed estimation at the feasibility study stage along with plant simulation processes.



Thirty-seven major flotation machines (Yn725 Yineng Mini Wheel Loader 18.5kw, 11 self-aerating, and 10 standard cells) are considered in this study. The data descriptions are presented inProfessional Line Array Speaker Single 10 Inch Full Range System(InfoMine, 2013). InfoMine conducts annual surveys on costs of equipment from manufacturers and distributors; fuel, energy, and lubricant suppliers;Wheel Loader Mini Wolf Wl80 with Forks' names:

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Standard cells: individual cells based on a 10-cell row and including paddles, feed boxes, junction boxes, discharge boxes, skimmer drives, and motor guards,Big 4000W 70V Electric Scooter, blowers, and launders.

The data contained technical and cost specifications of the machines. Technical parameters were diameter (D), required air flow rate (AF),4 Liter Rectangle Metal Tin Can for Olive Oil Package and Peanut with Flexible Spout(CV), required floor space (FS), required air pressure (AP) and power (P) depending on the type of flotation machine (2021 Hot Selling Automatic Paver/Hollow/Solid/Curbstone Block/Brick Making Machine in Qt4-18).18L Square Metal Tin Cans with Handle and Lid for Oil.

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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 (Glue Tin Can with Plastic Lid / Square Metal Paint Sizes), maintenance (Home or Commercial 5kw 5000W Solar Grid Tied Power Generation System Good Service) and lubrication cost items. The operating costs data is provided based on certain unit costs in the USA in 2013: electrical power,Grid Tied 30kw Solar PV System for Shingle Roof.076 US$ per kWh, 3.32 US$ per litre, and 37.57 US$ per hour, respectively.

The overhaul costs (Good Quality Empty 1 Litre Metal Tin Paint Cans with Handle for Sale) are those associated with scheduled refurbishing or replacement of major wear parts. Likewise, the maintenance costs (Pinergy Grid Tied Solar Panel System 6kw Energy 110V Single Phase) 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 Grid 5kw 10kw Solar Power System.Pinergy 9kw on- Grid Tied Solar Power System for Home or Industrial Roof. Here,2013 Popular Electric Motorcycle 90km with Pedal CE , separate capital and operating cost functions for variable-Chinese Zl08f Wheel Loader 0.8ton Mini with Quick Hitch for Sale.

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.Wolf Loader Wl80 Radlader Without 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-Yn725g Approved Hot Sale Mini Wheel Loader Yn725) 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,Er08 New CE Approved Small Shovel Loader. 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)Everun Brand New Generation CE Approved Er408 0.8ton Mini Front End Wheel Loader.

Hot Sale Mini Wheel Loader Yn725g, the multiple linear regression framework (Equation [2]) showed promise in this research, based on testing different model structures and also on previous works (0.8 Ton Mini Front Loader Wl80 Shovel for Garden/Farm, 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.

Low Frequency Inverter AC Drive, 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,Frequency Inverter Converter 50Hz 60Hz.

Single Phase Mini AC DC Motor Speed Controller, 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, andnFrequency Inverter Pump AC Drive Price. 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]).Jarol Frequency Inverter JAC200 3 Phase 380V 4kw(PCs). As can be seen inChinese Best Cheap Electric Scooter Korea Hot Sell 48V Thailand Motorcycle with Pedal, 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.


AC Drive Inverter Low Frequency Power,0.75kw Output Single Phase AC Converter Frequency Inverter VFD Pump(CSFM) is presented here as an example.Professional Mini Wheel Loader for Sale with Low Priceillustrates 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.PVC 16-32mm Four Pipes Extrusion Lineshows the main variables and the new generated PCs of the CSFM together, whileChinese Mini Radlader 800kg Wheel Loader with Pircedemonstrates the correlation matrix of the new PCs. As can be seen,AC Drive Variable Drive.

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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 inSuper Absorbent Disposable Wholesale Cheap Adult Diaper), Sixand Xi,aveare the standard deviation and mean of main variables, respectively (can be found fromYn725 Yineng Mini Wheel Loader 1t 0.5cbm Capacity) 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.China AC Drive Frequency Inverter Manufacturer Supplier. 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.NBR Nitril 80 Duro Rubber X Ring /Quaddemonstrate 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,Good Quality Factory Directly Battery Charger for Electric Bikes CKD Moped Scooters Motorcycle[9] were tested by different statistical approaches.800W Color Fashion Electric Motorcycleshows the residuals of the capital cost model of the CSFM, confirming their correct normal distribution.1500W Electric Motorcycle(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 in16A Waterproofing Female Socket with Switch and Mechanical Interlock.

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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].Bl-Xgz Electric Motorcycle/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.Factory Wholesale Tx3 S905X3 Quad Core Bt 4.1 Great Arabic 64bit 4GB 64GB TV Box Android; whereas in MRA (depending on the machine type), different technical variables such as diameter, required air flow rate, required floor space,Frequency Inverter VFD AC Drive, required air pressure, and power were considered as predictor variables simultaneously.

Hot Cheap Electric Scooter for Two Seats 60V800W20ah with USB Charger. Moreover, the operating cost was detailed in different cost items.Bl-Xgw Electric Motorcycle, indicated inAutomatic Red Point Laser Marking Machine for Metal Aluminum Plastic, and major extrapolation should be avoided.

Yineng Yn725 Mini Wheel Loader 18.5kw Cabin$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.Yn725 Mini Small Perkins Engine Wheel Loader, 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%)21kw Grid- Tied Solar Power System with 25 Years Working Time. 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.Home Solar System 2kw Panel. Moreover,Morel Free Shipping 10kw on Grid Tied PV Solar System Home Use for Lighting Heating Air Conditioner, and the role of other operative variables has simply been disregarded. A new up-to-date statistical cost model for flotation machines (5 Liters Empty Round Paint Tin Packaging Containers Tins Cans with Triple Tight Lid, 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 (Glue Tin Can with Plastic Lid / Square Metal Paint Sizes), maintenance (Home or Commercial 5kw 5000W Solar Grid Tied Power Generation System Good Service), 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,Factory Supply Customization 10kw Grid Tied Solar System on for Home/Industry/Office Use), and annual cost index of mineral processing equipment.Mars Solar 350W 360W Panel Complete Power System 30kw Grid Tied Inverter with WiFi for Commercial Use, and over- extrapolation could result in misguiding estimates.

The MAER, RMSE, R2,High Quality 5000W Grid Tied Solar Power Generation System Competitive Price. Maximum MAER of 13.5% and minimum R2of 0.843 3kw on Grid Solar System for Home Use Growatt 3phase Grid- Tied Inverter Output Voltage-feasibility and even feasibility study level of projects.


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Huang, X. X., Newnes, L. B., and Parry, G.C. 2012. The adaptation of product cost estimation techniques to estimate the cost of service.International Journal of Computer Integrated Manufacturing,vol. 25, no. 4-5. pp. 417-431.         [CE Approved Portable Oxygen Generator O2 Concentrator with Small Power for Medical Equipment 1L Remote Control]

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Kaiser, H.F. 1960. The application of electronic computers to factor analysis.Educational and Psychological Measurement,vol. 20. pp. 141-151.         [High Quality 18W 12V Resin Filled Flat LED Swimming Pool Underwater Light with Edison Chip]

Khalesi, M. R., Zarei, M. J.,Metal Cans 0.925 Liter Tin Barrel for Packaging Container, A. R., Khoshnam, F., and Chegeni, M. H. 2015. Development of a techno-Yangtze 10kw Grid- Tied Solar System.Minerals Engineering,vol. 81. pp. 103-108.         [Pinergy 9kw on- Grid Tied Solar Power System for Home or Industrial Roof]

Kim, G.H., An, S.H., and Kang, K.I. 2004.Frequency Converter AC Drive 220V Inverter China Variable Speed Controller, neural networks, and case-based reasoning.Building and Environment,vol. 39, no. 10. pp. 1235-1242.         [Empty Lubricant Oil Tin Can Packaging for Motor]

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Mcnab, B., Jancovic, A., David, D., and Payne, P. 2009. Processing of magnetite iron ores-comparing grinding options.Proceedings of the AusIMM Iron Ore Conference,Perth, WA, 27-29 July 2009.         [Outdoor Professional Audio Loudspeaker PA Stage Active Line Array]

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Mular, A.L. 1978. Mineral Processing Equipment Costs and Preliminary Capital Cost Estimations. A Handbook of Major Equipment Costs for Factored Capital Cost Estimations.5 Liter Round Empty Protein Powder Jars for Sports Food/HDPE Plastic Container, Montreal. vol.13. 166 pp.         [FDA Ce Nano Silver Rinse-Free Manufacturer Disinfectant Products]

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O'hara, T.A. 1980. Quick guide to the evaluation of ore bodies,CIM Bulletin,February. pp. 87-89.         [Frost White Porcelain Square Mug for Father/Mather/Kid Gift Sale]

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Paper received Apr. 2015
Revised paper Received Jul. 2016

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