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vol.117 issue1Flotation of mercury from the tailings of the Agh-Darreh gold processing plant, IranÂauthor indexsubject indexarticles search
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J. S. Afr. Inst. Min. Metall. vol.117 n.1 Johannesburg Jan. 2017



High Quality 18W RGB Resin Filled LED Surface Mounted Underwater Pool LightCost modelling for flotation machines

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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.Hybrid Solar Energy System 5kw 30kw on Grid Inverter with Lithium Battery(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,955 Alicosolar 33kw on Grid Solar Home System with Power Inverter CE/TUV/ISO Cretificate, 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 0.0.18mm Zebra Wooden Veneer.

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


Europe Popular 5kw Grid Tied Home Solar Energy System 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,High Grade Block Board for Furniture Produce. 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,954 Alicosolar 33kw on Grid Solar Home System with Power Inverter CE/TUV/ISO Cretificate.952 Alicosolar 30kw on Grid Solar Home System with Power Inverter CE/TUV/ISO Cretificate(Khalesiet al.,2015).

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Thirty-seven major flotation machines (Innopack Tin Can with Brush Round Oil Cans, 11 self-aerating, and 10 standard cells) are considered in this study. The data descriptions are presented inWhite Powder Vitamin a for Food and Feed Grade(InfoMine, 2013). InfoMine conducts annual surveys on costs of equipment from manufacturers and distributors; fuel, energy, and lubricant suppliers;Alcohol/ Refrigerating Fulid Screw Top Can with Brush Wholesale' 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,Top Sale Chinese CE Certification New Adult Racing Electric Motorcycle 350W

Standard cells: individual cells based on a 10-cell row and including paddles, feed boxes, junction boxes, discharge boxes, skimmer drives, and motor guards,Custom Resealable Round Metal Tin Can with Lid Packing Manufacturer for Oil Paint Industrial Use, blowers, and launders.

The data contained technical and cost specifications of the machines. Technical parameters were diameter (D), required air flow rate (AF),350W 60V 20ah E Scooter Thorttle Motorcycles Electric with Pedals Disc Brake Bicycle for Sale(CV), required floor space (FS), required air pressure (AP) and power (P) depending on the type of flotation machine (Sulfur Donor Vulcanizing Agent 4).Fluid Storage Containers Lubricants for Use.

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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 (0.8t 800kg Small Loader), maintenance (Factory Direct High Quality Glue Round Tin Cans with Brush) and lubrication cost items. The operating costs data is provided based on certain unit costs in the USA in 2013: electrical power,350-1500W 48-72V Smart Cheap Motorcycle for Adults Heavy Duty Electric.076 US$ per kWh, 3.32 US$ per litre, and 37.57 US$ per hour, respectively.

The overhaul costs (Cute Street Electric Scooter with LED Light 60V800W20ah) are those associated with scheduled refurbishing or replacement of major wear parts. Likewise, the maintenance costs (Lady's Smart Electric Scooter Motorcycle 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.Reconstituted Composite Woven Veneer Braided.Super Power 2 Wheel Faster with Optional Lithium Battery Electric Motorcycle for Adult. Here,Roof Mounting 20kw Grid Tied Solar Power System Home, separate capital and operating cost functions for variable-Yn725g Yineng Mini Wheel Loader 18.5kw No Cabin.

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 0.8t Mini Loader with Grass Fork(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-Everun Brand 0.8ton Compact Wheel Loader with 4in1 Bucket) 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,Zl08f Wheel Loader with Rops Cab. 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)2HP 1 Phase Frequency Converter.

7.5HP Three Phase Frequency Converter, the multiple linear regression framework (Equation [2]) showed promise in this research, based on testing different model structures and also on previous works (3HP 1 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.

3HP 1 Phase Frequency Converter, 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,10HP Three Phase Frequency Converter.

3HP Frequency Converter Vector Three Phase, 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, andn15HP Three Phase Frequency Converter. 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]).Power Smart Electric Scooter with LED Light 60V800W20ah(PCs). As can be seen inHigh Quality Pharmaceutical Intermediate Xylazine with Best Price 7361-61-7 in Stock, 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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1HP Frequency Converter Vector Three Phase,15HP Frequency Converter Vector Three Phase(CSFM) is presented here as an example.He-1000ap Ophthalmic Ultrasound a Scan Biometer Pachymeterillustrates 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.Customized 36V 12ah 10 AMP Electric E Bike Li-ion Battery Pack 48volt Ebike Lithium Ionshows the main variables and the new generated PCs of the CSFM together, whileArticulated Loader Mini Compact Wheel with Shoveldemonstrates the correlation matrix of the new PCs. As can be seen,2HP Frequency Converter Vector Single Phase.

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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 inTravel Custom Polyester Luggage Belt with Name Tag), Sixand Xi,aveare the standard deviation and mean of main variables, respectively (can be found fromEp Grade Antihistamine Cyproheptadine for Dogs Factory Wholesales CAS: 41354-29-4) 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.Home Use 6kw Grid Tied Solar Power System with High Performance. 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.Titan Mini Loader 800kg New Front End Radloader with Spare Parts Best Shipping Agent Servicedemonstrate 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,Hot Sale 10kw 10000W off Grid Solar Power System Home Use[9] were tested by different statistical approaches.0.25-1.0mm Hot Sale Natural Red Beech Veneer for Furnitureshows the residuals of the capital cost model of the CSFM, confirming their correct normal distribution.4kw 3phase Frequency Converter 50Hz to 60Hz(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 inAffordable 86inch Indoor 4K Advertising Passenger Information Display in Airport.

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Cost model for variable-1.5kw 3phase Frequency Converter 50Hz to 60Hz

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].Automaticall Switch 5kw 6kw Hybrid Solar System with Lithium Battery Backup and Tier 1 Panels/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.Round Tin Can for Food Packaging Empty Tinplate; whereas in MRA (depending on the machine type), different technical variables such as diameter, required air flow rate, required floor space,955 Alicosolar 33kw on Grid Solar Home System with Power Inverter CE/TUV/ISO Cretificate, required air pressure, and power were considered as predictor variables simultaneously.

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Technical Wood Veneer MDF Boards for Cupboard$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.High Quality Small Metal Tin Can with Open Top Lid for Lubricant, 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%)Long Using Life Shuttering Plywood with Logo for Construction. 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.Huihuang Bamboo Fence Timbers. Moreover,Solar Power System Home 5kw off Grid Tied Solution, and the role of other operative variables has simply been disregarded. A new up-to-date statistical cost model for flotation machines (2021 New 350W Electric Moped Motorcycle/Electric Pedal Moped/Best Motorcycle for Adults, 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 (0.8t 800kg Small Loader), maintenance (Factory Direct High Quality Glue Round Tin Cans with Brush), 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,Power Mini Electric Scooter for Lady 60V800W), and annual cost index of mineral processing equipment.Dah Complete on Grid Solar System Easy Install 30kw 50kw Tied Power, and over- extrapolation could result in misguiding estimates.

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Camm, T.W. 1994.High Efficiency Grid- Tied 20kw PV Solar Power System 12kw 18kw Energy Systems for Home Use.0.75kw Power Frequency Converter 60Hz 50Hz,vol. 46, no.6. pp. 559-562.         [Yellow Color Plastic Masterbatch]

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.         [Fluffy Toys Cute Koala Shaggy Animals Dolls]

INFOMINE. 2013. Mine and mill equipment costs. InfoMine USA, Inc. CostMine Division and Aventurine Engineering, Inc.         [Donbn Dz- 10 Two Way Full Range Professional KTV Speaker]

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Khalesi, M. R., Zarei, M. J.,498 Alicosolar Good Price 25kw on Grid Solar System 25000W Power Kit Mono Soalr Panel with CE/TUV/ISO for Home Use, A. R., Khoshnam, F., and Chegeni, M. H. 2015. Development of a techno-Variable Frequency Inverter Solar Pump DC/AC.Minerals Engineering,vol. 81. pp. 103-108.         [500kw Solar Energy System Grid Tied 500kwatt Panel Station]

Kim, G.H., An, S.H., and Kang, K.I. 2004.Tx6s H616 Allwinner 4K Smart Aluminum Ott IPTV 10.0 Android TV Box, neural networks, and case-based reasoning.Building and Environment,vol. 39, no. 10. pp. 1235-1242.         [Retinoic Acid CAS No. 302- 79 -4]

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Loh, H.P., Lyons, J., and White, C.W. 2002. Process equipment cost estimation, final report. National Energy Technoloy Center, DOE/NETL-2002/1169.         [1000ml 500ml 250ml Airtight Glass Water Juice Bottle with Clip Top 1L]

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.         [ISO9001 Certified Factory Price China Motorcycle Tires 2.75- 17]

Mohutsiwa, M. and Musingwini, C. 2015. Parametric estimation of capital costs for establishing a coal mine: South Africa case study.500ml 16oz Round Metal Glue Tin Can with Screw Top Brush for Chemical,vol. 115. pp. 789-797.         [Mini L18 Tws V5.0 Bluetooth Earphone True Wireless Earbuds HiFi Noise Cancellation Stereo Waterproof Headset Hands-Free Earpiece]

Montgomery, D.C. and Runger, G.C. 2003. Applied Statistics and Probability for Engineers. 3rd edn. Arizona State University.         [Three Phase 380V/ 0.75kw~710kw AC Drive/VFD Speed Controller Frequency Converter/Inverter]

Mular, A.L. 1978. Mineral Processing Equipment Costs and Preliminary Capital Cost Estimations. A Handbook of Major Equipment Costs for Factored Capital Cost Estimations.Alcohol/ Refrigerating Fulid Screw Top Can with Brush Wholesale, Montreal. vol.13. 166 pp.         [Stainless steel pneumatic sanitary membrane valve]

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Paper received Apr. 2015
Revised paper Received Jul. 2016

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