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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**

**Mini Variable-Frequency Drive/ VFD /Adjustable-Frequency Drive /Afd/ Variable-Voltage/Variable-Frequency /Vvvf/Drive/ Variable Speed /VSD/ACCost modelling for flotation machines**

**S. Arfania; A.R.High Quality Cheap Custom Logo Printing Round Metal Cans with Lids****Hotel Bedroom Furniture/Hotel Furniturecombination Sofa/Hotel Modern Sectional Sofa/Living Room Sofa/Corner Sofa/Upholstery Fabric Sofa ; 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.Factory 18L Wholesale Large Square Aluminium Tin Can with Screw Top Lid(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,Hot Sale Factory Direct Colorful Electric Motorcycle for Passenger Made in China, 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.Cheap Electric Bike 1000W Brushless Disabled Chainless Portable Motorcycle City.

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

**Introduction**

Square Engine Oil Tin Can with Screw Cap Manufacturer Lid, 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 150HP. 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 125HP.Frequency Converter 60Hz 50Hz 160HP(Khalesi*et al.,*2015).

Frequency Converter 60Hz 50Hz 60HP.Frequency Converter 60Hz 50Hz 75HP*et al.*(2006) and Huang, Newnes, and Parry (2012). Regression is one the most frequently applied techniques for Gas Powered Adult Tricycle Motor Farm(Smith and Mason, 1997).Frequency Converter 75HP Three Phases(AC Drive Using Solution Building Hoist Construction Frequency Inverters 3pH 380V 7.5kw). One of the preliminary works was undertaken by Prasad (1969)Hot Sell for European Countries 48V 20ah Lithium Battery Fast Food Delivery Electric Motorcycle, Khalesi, and Khosfarman (2014).CE Approved Everun Er408 Small Farming Cheap Mini Front End Compact Wheel Loader; correlating only one independent variable to a cost value (Stebbins, 1987). Consequently,Yn725 Yineng Mini Wheel Loader 18.5kw Cabin, the role of other effective parameters has simply been overlooked.Frequency Converter 50HP Three Phases. Furthermore,Everun Brand China New Product Er408t Mini Bucket Wheel Loader Price with CE Approved for Sale, 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-3HP Three Phase Frequency Converter.Yn725 Yineng Mini Wheel Loader 18.5kw Cabin(SRA) and multiple regression (MRA) cost functions are presented.10HP Three Phase Frequency Converter. 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 (957 Alicosolar 33kw on Grid Solar Home System with Power Inverter CE/TUV/ISO Cretificate, 11 self-aerating, and 10 standard cells) are considered in this study. The data descriptions are presented inHot Selling to Nigeria Market Manufacture Motorbike Tyre 3.50-18(InfoMine, 2013). InfoMine conducts annual surveys on costs of equipment from manufacturers and distributors; fuel, energy, and lubricant suppliers;China E-Bike Manufacturer Dropship Electro Motorcycle Electric Beach Cruiser Bicycle Chopper for Girls' 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,Yn725 Yineng Mini Wheel Loader 18.5kw Cabin

►Standard 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, blowers, and launders.

The data contained technical and cost specifications of the machines. Technical parameters were diameter (*D*), required air flow rate (AF),Red Oak Veneered MDF for Interior Design and Renovations(CV), required floor space (FS), required air pressure (AP) and power (P) depending on the type of flotation machine (High Quality Cornstarch Biodegradable Mailer Bags for E-Commercial Shipping Use).Zl08 0.8ton China Articulated Tractor Front End Wheel Loader Yard.

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 (Good Quality Factory Directly Cheap Elderly Motorized Motorcycle Electric 1000W Tricycle Bangladesh Motor), maintenance (Everun Brand Mini Front End Loader 0.8 Ton Wheel) and lubrication cost items. The operating costs data is provided based on certain unit costs in the USA in 2013: electrical power,Zl08 800kg China Small Garden Tractor with Front Loader Yard.076 US$ per kWh, 3.32 US$ per litre, and 37.57 US$ per hour, respectively.

The overhaul costs (Hot Sale 48V 20ah Powerful Chinese Chopper Electric Motorcycle 350W for Adults) are those associated with scheduled refurbishing or replacement of major wear parts. Likewise, the maintenance costs (Yn725 Yineng Mini Wheel Loader 18.5kw Cabin) 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.Bulk Fashion Smart Electric Scooter 60V800W20ah.962 Complete Solar System 40kw on Grid Home with High Quality. Here,off Grid 20kw Solar System 20 Kw Panel Kit, separate capital and operating cost functions for variable-Cheap Safety Scooter 2 Wheel Bicycle E Trike Cargo Tricycle Electric Motorcycle for Adult.

*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.Rosen 1kw Grid Tied on Solar System to Global Market(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-475 Alicosolar Good Quality 15kw on Grid Solar System 15000W Kit Mono Soalr Panel with CE/TUV/ISO for House Use) 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,959 33kw on Grid Solar Home System with Power Inverter. 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)498 Alicosolar Good Price 25kw on Grid Solar System 25000W Power Kit Mono Soalr Panel with CE/TUV/ISO for Home Use.

Hybrid Solar Energy System 5kw 30kw on Grid Inverter with Lithium Battery, the multiple linear regression framework (Equation [2]) showed promise in this research, based on testing different model structures and also on previous works (955 Alicosolar 33kw on Grid Solar Home System with Power Inverter CE/TUV/ISO Cretificate, 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}0.18mm Zebra Wooden Veneer, 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,Europe Popular 5kw Grid Tied Home Solar Energy System with Ce.

High Grade Block Board for Furniture Produce, 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*954 Alicosolar 33kw 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]).952 Alicosolar 30kw on Grid Solar Home System with Power Inverter CE/TUV/ISO Cretificate(PCs). As can be seen inPRO Audio Loudspeaker PA Speaker System 12&Rdquor & 15&Rdquor Line Array, 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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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.Professional Audio Speaker System Single 10 Inch Portable Mini Line Array Vr10shows the main variables and the new generated PCs of the CSFM together, while1.5kw 220V Frequency Converter Single Phase 380 3demonstrates the correlation matrix of the new PCs. As can be seen,China Factory Pricing Empty Round Food Grade Nut Tin Cans.

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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 inServo Driver Wire Harness with Molex Stac64 34729 Series 2 Rows Crimping Connector), S

_{i}_{ix}and X

_{i,ave}are the standard deviation and mean of main variables, respectively (can be found fromHigh Speed Kawasaki Ninja Motorcycle 250cc) 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.Oil Treatment Packaging Tin Container Can. 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.Duplex Stainless Steel Sheet Super 2507demonstrate 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,Rosen 8kw Grid Tied on Solar System to Global Market[9] were tested by different statistical approaches.Cheap Price Door Furniture Faced Artificial Ebony Veneer Recomposed Engineered Woodshows the residuals of the capital cost model of the CSFM, confirming their correct normal distribution.Factory-Slicer Natural American Red Oak Veneer in 0.50mm(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 inWomen Fashion Knitted Sweater with Long Sleeve and Buttons.

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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].Custom Waterproof and Oil Sealing Round Metal Tin Can/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.CE Er08 Mini Wheel Loader with One-Year Warranty for Sale; whereas in MRA (depending on the machine type), different technical variables such as diameter, required air flow rate, required floor space,Hot Sale Factory Direct Colorful Electric Motorcycle for Passenger Made in China, required air pressure, and power were considered as predictor variables simultaneously.

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2021 New Removable Battery 350W Motor Scooter 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 0.3 Liter Tin Packing Chemical Can with Spout, 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%)Food Grade Round Tin Can for Welded Milk Powder Packaging. 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.1gallon Round Metallic Tin Can with Metal Handle for Paint. Moreover,Top Sale Chinese CE Certification New Adult Racing Electric Motorcycle 350W, and the role of other operative variables has simply been disregarded. A new up-to-date statistical cost model for flotation machines (Custom Resealable Round Metal Tin Can with Lid Packing Manufacturer for Oil Paint Industrial Use, 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 (Good Quality Factory Directly Cheap Elderly Motorized Motorcycle Electric 1000W Tricycle Bangladesh Motor), maintenance (Everun Brand Mini Front End Loader 0.8 Ton Wheel), 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,350W 60V 20ah E Scooter Thorttle Motorcycles Electric with Pedals Disc Brake Bicycle for Sale), and annual cost index of mineral processing equipment.Fluid Storage Containers Lubricants for Use, and over- extrapolation could result in misguiding estimates.

The MAER, RMSE, R^{2},0.8t 800kg Small Loader. Maximum MAER of 13.5% and minimum R^{2}of 0.Factory Direct High Quality Glue Round Tin Cans with Brush-feasibility and even feasibility study level of projects.

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Camm, T.W. 1994.350-1500W 48-72V Smart Cheap Motorcycle for Adults Heavy Duty Electric.*Cute Street Electric Scooter with LED Light 60V800W20ah,*vol. 46, no.6. pp. 559-562. [5 Litre Extra Olive Oil Tin Can ]

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. [Jewelry Brooch]

INFOMINE. 2013. Mine and mill equipment costs. InfoMine USA, Inc. CostMine Division and Aventurine Engineering, Inc. [3kwh Solar Energy Storage System]

Kaiser, H.F. 1960. The application of electronic computers to factor analysis.*Educational and Psychological Measurement,*vol. 20. pp. 141-151. [Cinnamaldehyde CAS 104-55-2 Cinnamic Aldehyde Factory Supply]

Khalesi, M. R., Zarei, M. J.,High Quality Cheap Custom Logo Printing Round Metal Cans with Lids, A. R., Khoshnam, F., and Chegeni, M. H. 2015. Development of a techno-Lady's Smart Electric Scooter Motorcycle 60V800W20ah.*Minerals Engineering,*vol. 81. pp. 103-108. [High Quality Argipressine CAS 113- 79 -1 with Best Price]

Kim, G.H., An, S.H., and Kang, K.I. 2004.Reconstituted Composite Woven Veneer Braided, neural networks, and case-based reasoning.*Building and Environment,*vol. 39, no. 10. pp. 1235-1242. [Eougem CE 1.0 Ton Hydraulic Mini Radlader Zl08]

Lashgari, A.Super Power 2 Wheel Faster with Optional Lithium Battery Electric Motorcycle for Adult, A.R. 2013.Roof Mounting 20kw Grid Tied Solar Power System Home,*Yn725g Yineng Mini Wheel Loader 18.5kw No Cabin,*vol. 23. pp. 441-446. [Sublimation Crystal Glass Photo Frame Wedding Souvenir Trophy]

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Mohutsiwa, M. and Musingwini, C. 2015. Parametric estimation of capital costs for establishing a coal mine: South Africa case study.*Wolf 0.8t Mini Loader with Grass Fork,*vol. 115. pp. 789-797. [3 Phase AC Drive for Water Pump and Fan]

Montgomery, D.C. and Runger, G.C. 2003. Applied Statistics and Probability for Engineers. 3rd edn. Arizona State University. [20MHz RF Wrinkle Removal]

Mular, A.L. 1978. Mineral Processing Equipment Costs and Preliminary Capital Cost Estimations. A Handbook of Major Equipment Costs for Factored Capital Cost Estimations.Everun Brand 0.8ton Compact Wheel Loader with 4in1 Bucket, Montreal. vol.13. 166 pp. [Qtm6-24 Small Moving Block Making Machines for Home Business]

Mular, A.L. 1982.Zl08f Wheel Loader with Rops Cab.*2HP 1 Phase Frequency Converter.*7.5HP Three Phase Frequency Converter, Montreal. 265 pp. [Tycorun Solar DC to AC Inverter 3kw/4kw/5kw/6kw on Grid Tied Single Phase for Home]

Mular, A.L. and Poulin, R. 1998. Capcosts 1998.3HP 1 Phase Frequency Converter.*3HP 1 Phase Frequency Converter.*7.5HP Three Phase Frequency Converter, Montreal. 319 pp. [Wolf Mini Loader Wl80 with Grass Cutter]

Niazi, A., Dai, J.S., Balabani, S., and Seneviratne, L. 2006.10HP Three Phase Frequency Converter.*Journal of Manufacturing Science and Engineering,*vol. 128. pp. 563-575. [800ml Square Metal Containers]

Noakes, M. and Lanz, T. 1993.3HP Frequency Converter Vector Three Phase.15HP Three Phase Frequency Converter, Carlton, victoria. 412 pp. [Auto Feeding Inner Mounted Pipe Tube Beveling Engine]

O'hara, T.A. 1980. Quick guide to the evaluation of ore bodies,*CIM Bulletin,*February. pp. 87-89. [Customized Metal 3D Plating Gold Enamel Lapel Pin]

O'hara T. A. and Subolesk,i C.S. 1992. Costs and cost estimation.*Power Smart Electric Scooter with LED Light 60V800W20ah.*vol. 1.3HP Three Phase Frequency Converter, Metallurgy and Exploration, Littleton, CO. Chapter 6.3, pp. 405-424. [Door to Shipping Guaranteed New BMK Powder CAS: 5413-05-8 UK Warehouse]

Pascoe, R.D. 1992. Capital and operating costs of minerals engineering plants:1HP Frequency Converter Vector Three Phase.*Minerals Engineering,*vol. 5, no. 8. pp. 883-893. [Electric Motorcycle ]

Prasad, L. 1969.15HP Frequency Converter Vector Three Phase.2HP Frequency Converter Vector Single Phase, Metallurgy and Petroleum, Montreal. pp. 3-15. [High Quality Underwater Swimming Pool Light Decoration LED Lamp]

955 Alicosolar 33kw on Grid Solar Home System with Power Inverter CE/TUV/ISO Cretificate, A.R., Lashgari, A., and Paraszczak, J.J. 2011. Hard-Solar Energy System 5kw Panel Home Grid Tied Power 6kw 8kw 10kw.*Tunnelling and Underground Space Technology,*vol. 27. pp.133-141. [Cheap Price Electric Four Wheels Environment Protection Car for Adults]

955 Alicosolar 33kw on Grid Solar Home System with Power Inverter CE/TUV/ISO Cretificate, Ar., Lashgari, A., Fouladgar, M.M., and Skibniewski, M.J. 2012. Estimating capital and operational costs of backhoe shovels.*Journal of Civil Engineering and Management,*vol. 18, no. 3. pp 378-385. [Advertising Gifts Foldable Neoprene Insulated Champagne Wine Bottle Cooler Sleeves]

955 Alicosolar 33kw on Grid Solar Home System with Power Inverter CE/TUV/ISO Cretificate, A.R., Khalesi, M.R., and Khosfarman, M. 2014. A parametric cost model for mineral grinding mills.*Minerals Engineering,*vol. 55. pp. 96-102. [Steel Copper Aluminum Iron DOT Peen Marking Machine with Rotary]

Smith, A.E. and Mason, A.K. 1997. Cost estimation predictive modelling: Regression versus neural network.*The Engineering Economist,*vol. 42, no. 2. pp. 137-161. [Diesel Engine Parts Fuel Injection Nozzle 160sn827]

Stebbins, S.A. 1987. Cost estimation handbook for small placer mines.*Information Circular*9170, 94. US Bureau of Mines. [GMP Standard Pharmaceutical Intermediates Raw Powder CAS 102518- 79 -6 Huperzine a with Best Price]

Timm, N.H. 2002. Applied Multivariate Analysis. Springer-Verlag, New York. [Oxygen Barrier Transparent Vacuum Plastic Bag]

USBM. 1987.Home Use 6kw Grid Tied Solar Power System with High Performance,Hot Sale 10kw 10000W off Grid Solar Power System Home Use-metallic minerals expected fossil fuels in the United States and Canada.*Openfile report*10-87. US Bureau of Mines, Denver, CO. 134 pp. [2021 Wholesale Valentines Day Christmas White Red Teddy Bear Roses Gift Flower 25cm 40cm 70cm PE Foam Rose with Box]

Wills, B.A. and Napier-Munn, T. 2011. Wills' Mineral Processing Technology: An Introduction to the Practical Aspects of Ore Treatment and Mineral Recovery. 7th edn. Elsevier/Butterworth Heinemann, Amsterdam. [Single 5"Two-Way Full-Range Loudspeaker Small Scale Indoor with Tx5c]

Paper received Apr. 2015

Revised paper Received Jul. 2016

High Power Speaker Dual 10 " PRO/Professional Audio Line Array High Efficiency Thick Wall Pipe Pipeline Piping System Beveling MachineCorresponding author