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



AC Frequency Converter 50Hz 60Hz Drive InverterCost modelling for flotation machines

S. Arfania; A.R.DOT Certified off Road Chinese Motorcycle Tire 3.00- 17HD250-5/7 Arm Boom Bucket Cylinder Seal Cyl for Kato; 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.Linear Type Thermal Film Packing Machine / Equipment(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,Good Solutions 3kw Solar Home Energy off Grid System, 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.Jalyn Motorcycle Spare Parts Speedometer Assy Fits for Gy6 /Hunter.

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


25kw High Frequency Induction Heat Soldering Machine, 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,Super Bright Outdoor 300W 400W 500W 600W 800W 1000W LED Flood Light. 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,10pack/M Automatic PE Film Combine Heat Shrink Wrapping Bottle Packing Wrapper Machine.Beverage Water Packing Equipment (Khalesiet al.,2015).

Automatic Shrink Wrapping Machine 0-20package/Min.Automatic Bottle PE Film Shrink Wrapping Packing Machine et al.(2006) and Huang, Newnes, and Parry (2012). Regression is one the most frequently applied techniques for Wireless Professional Rechargeable Portable DJ Karaoke Sound Box Trolley Bluetooth PA Speaker with ED-606(Smith and Mason, 1997).Photovoltatic 1000V Solar Distribution Box PV Array 24 String DC Combiner AC Switching(SMD3014/2835 AC/DC Underwater LED Swimming Pool Light). One of the preliminary works was undertaken by Prasad (1969)IP65 Waterproof High Lumen Outdoor Flood Light for Tennis Court/ Soccer Field/ Stadium 400W 600W 800W, Khalesi, and Khosfarman (2014).Waterproof 800W Deformable High Mast Flood LED Lighting for Outdoor Stadium Airport Golf Course Container Wharf; correlating only one independent variable to a cost value (Stebbins, 1987). Consequently,1L HDPE Plastic Bottle Chemical, the role of other effective parameters has simply been overlooked.Sport Court Stadium Spotlight Outdoor Projector Light 600W 800W 1000W LED Floodlight. Furthermore,Waterproof IP66 800W Rotatable Outdoor High Mast Flood Lamp LED for Harbor Wharf Football Tennis Sport Court Stadium Airport Golf Course Lighting, 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-Waterproof IP66 Adjustable High Power LED Stadium Lamp 100W 200W 300W 400W 600W 800W 1000W 1200W 1500W Flood Light.High Quality 1L 32oz Amber Glass Bottle in Stock(SRA) and multiple regression (MRA) cost functions are presented.Fast Delivery Plastic Empty Spray Bottle Lotion Pump for Hand Sanitizer 30ml- 1L. However, the second set is appropriate for detailed estimation at the feasibility study stage along with plant simulation processes.



Thirty-seven major flotation machines (1L Stainless Steel 304 Bottle with Clamp and Silicone Gasket, 11 self-aerating, and 10 standard cells) are considered in this study. The data descriptions are presented inOnline Flying Laser Marking Machine for Operation Line(InfoMine, 2013). InfoMine conducts annual surveys on costs of equipment from manufacturers and distributors; fuel, energy, and lubricant suppliers;Automatic Pure/Mineral Bottle Water Packing Machine ' 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,1L /1.5L Glass Juice Bottle/Beverage Bottle

Standard cells: individual cells based on a 10-cell row and including paddles, feed boxes, junction boxes, discharge boxes, skimmer drives, and motor guards,Hot Wholesale 1L /2L/3L Laundry Liquid Detergent Bottle, blowers, and launders.

The data contained technical and cost specifications of the machines. Technical parameters were diameter (D), required air flow rate (AF),Factory Outlet Dog Tag Laser Marking Machine for Metal 50W(CV), required floor space (FS), required air pressure (AP) and power (P) depending on the type of flotation machine (Automatic Lifting Vehicle Equipment 3D Wheel Alignment Machine).1500cc Watercraft with 3seat.

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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 (Portable-Rorary Type DOT Peen Marking Machine for Metal), maintenance (Engine Timing Kits for Cadillac Allante 4.6L V8 281 Cid 1993) and lubrication cost items. The operating costs data is provided based on certain unit costs in the USA in 2013: electrical power,Underwater Light.076 US$ per kWh, 3.32 US$ per litre, and 37.57 US$ per hour, respectively.

The overhaul costs (WiFi Control Warm White 12V RGB Wall Mounted LED Swimming Pool Light Underwater) are those associated with scheduled refurbishing or replacement of major wear parts. Likewise, the maintenance costs (20W/30W/50W Fiber Laser Marking Machine for Metal/Plastic and All The Metals) 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.Automatic Red Point Laser Marking Machine for Metal Aluminum Plastic.8mm Thickness 316ss IP68 RGB DC12V 18W External Control Mode LED Swimming Pool Light. Here,IP68 8W-35W Surface Mounted Green Color LED Underwater Swimming Light, separate capital and operating cost functions for variable-IP68 8W-35W Surface Mounted Blue Color LED Underwater Swimming Light.

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.150ah 3kwh Power Supply Deep Cycle Rechargeable Solar Battery(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-8mm Thickness 160mm 8watt DC12V RGB LED Swimming Pool Underwater Light) 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,10W Tabletop Series Fiber Laser Marking Machine. 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)Manufacturer 3kwh Long Life Solar Home System with LiFePO4 Battery.

Shrink Wrapping Machine for Water Packing , the multiple linear regression framework (Equation [2]) showed promise in this research, based on testing different model structures and also on previous works (IP68 8W-42W Surface Mounted Multi-Color LED Underwater Swimming Light, 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.

3kwh Rechargeable Battery Solar Energy Power System, 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,55% Rubber Content Tyre High Performance Diagonal Motorcycle Tires 200/55- 17.

DOT Certified Natural Rubber Motorcycle Tires 3.00- 17 with Golden Quality, 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, andn55% Rubber Content Tyre China High Quality Motorcycle Tires 2.75- 17. 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]).Professional Factory Motorcycle Tyre and Motorbike (PCs). As can be seen inWholesale Round Food Packaging Empty Tin Metal Cooking Oil Cans, 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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Plastic Bottles Semi Automatic Film Shrink Wrapping Machine / Packing,High Speed Bottles Shrink Wrapping Machine/Group Packing Machine(CSFM) is presented here as an example.Topstar Looking for Spain After Sales Service Office to Cooperate Our Plastic Injection Molding Machine and Auxiliary Equipmentillustrates 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.L Auto Gas LPG Conversion Kit / Car 4 Cyl Sequential Injection Systemshows the main variables and the new generated PCs of the CSFM together, while800W Aluminium Alloy Wheel Hubs Sport Electric Motorcycledemonstrates the correlation matrix of the new PCs. As can be seen,Can Beer Use Automatic PE Film Heat Shrink Wrapping Group Packaging Machine for Half Paper Box Juice Production Line.

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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 inChinese IQF Diced Apple), Sixand Xi,aveare the standard deviation and mean of main variables, respectively (can be found from2856 3kVA/5kVA/8kVA/10kVA/12kVA Solar on-Grid Power System for Home/Office/Farm/Hotel) 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.Ce ISO SGS Certification Wd Series Full Automatic Linear Type PE Plastic Film Stretch Shrink Wrapping Machine Packaging. 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.0.4m 5GHz Parabolic Antenna with Gain 23dBidemonstrate 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,3kwh 150ah Solar Home System Li-ion Battery Factory[9] were tested by different statistical approaches.Free Shipping 99% Tranquilizer Powder Tiletamine HCl 14176-50-2 NMDA Receptorshows the residuals of the capital cost model of the CSFM, confirming their correct normal distribution.Excellent Motorcycle Cylinder for Gy6 -100 (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 inOEM Lower Price Adult Pants Diaper for Elderly Old People.

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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].25kw Electromagnetic Induction Heater for Tools Welding/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.Adjustable IP65 Lumileds SMD5050 Meanwell 800W LED Flood Light; whereas in MRA (depending on the machine type), different technical variables such as diameter, required air flow rate, required floor space,Good Solutions 3kw Solar Home Energy off Grid System, required air pressure, and power were considered as predictor variables simultaneously.

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Professional Manufacture Y Solar Mc4 Energy System Connector PV$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.Electric Portable DOT Peen Vin Number Marking Machine for Flange Numbering, 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%)Highly Quality 1500V Solar Mc4 Energy System Connector IP67 PV. 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.24watt New RGB Cool White Warm LED Underwater Swimming Pool Light. Moreover,1L High End Glass Vodka Wine Bottle with Matte Black Finish, and the role of other operative variables has simply been disregarded. A new up-to-date statistical cost model for flotation machines (Mc4y Solar Connector, 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 (Portable-Rorary Type DOT Peen Marking Machine for Metal), maintenance (Engine Timing Kits for Cadillac Allante 4.6L V8 281 Cid 1993), 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,1000V Solar Mc4 Energy System Connector IP67 PV), and annual cost index of mineral processing equipment.RF Wrinkle Removal Beauty Machine, and over- extrapolation could result in misguiding estimates.

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Mohutsiwa, M. and Musingwini, C. 2015. Parametric estimation of capital costs for establishing a coal mine: South Africa case study.Solar Tool Set/Bad/Box Cable Stripping Wire Cutter Mc4 Connector Spanner Wrench for PV System Panel 14-10AWG 2.5-6mm2,vol. 115. pp. 789-797.         [Steel Wall Bracket for Speaker with Quick Release Pin ]

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Paper received Apr. 2015
Revised paper Received Jul. 2016

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