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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**

**150ah Lithium Iron Phosphate Cost modelling for flotation machines**

**S. Arfania; A.R.Changhong Film Stack Flexo Printing Machine****Sy-AC51 Best Price 128 Elements Wireless Probe with Color Doppler; 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.Xft- 710 Axial Flow Fire Smoke Fan(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,Bt Sk Cat Straight Collet Power Multi-Lock Chuck Milling Holder Arbors, 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.Disperse Violet 26 Dyes.

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

**Introduction**

Skyzon® Cationic Violet 3R/Cationic Dyes/Cloth Dye, 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,Disperse Dyestuff Violet S3rl 200% C. I. 63. 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,Pigment Violet 1 or Fast Rose Toner/Fast Lake.Disperse Dyestuff Violet 200% P-CF for Textile(Khalesi*et al.,*2015).

Disperse Red/Blue/Orange/ Violet /Black.Disperse Dyestuff Violet Recp-Hf 100% for Textile*et al.*(2006) and Huang, Newnes, and Parry (2012). Regression is one the most frequently applied techniques for Hzm908 Jn 908 31.5loader Mini Wheel Loader for Sale Best Price Top Quality(Smith and Mason, 1997).Factory Cost Qualified Effect Antistatic Plastic Blue Color Masterbatches for Electronic Components(PA System Passive ABS 100V 8ohm 10W Wall Mount Horn Speaker Waterproof for Outdoor Use). One of the preliminary works was undertaken by Prasad (1969)Plastic Products Pellets Raw Granulesanti-Static Material Yellow Antistatic Masterbatch Customized Home Appliance, Khalesi, and Khosfarman (2014).Super Popular Endless Swimming Pool with Jacuzzi SPA for Market; correlating only one independent variable to a cost value (Stebbins, 1987). Consequently,Massage Bathtub, the role of other effective parameters has simply been overlooked.PA Filler Masterbatch for Injection Moulding. Furthermore,Swedish Soaking Bath Tubs Lowes Plastic Adult Freestanding Bathtub, 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-Laswim Endless Pool/Counter Flow Pool.Double Slipper Two Upper End Freestanding Soaking New Bath Tub(SRA) and multiple regression (MRA) cost functions are presented.Jacuzzi Massage Endless Swimming Pool Swim SPA. 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 (2021 Popular Great Large 5.95 Meter Swimming Pool Laswim Bathtub Hot Tub SPA, 11 self-aerating, and 10 standard cells) are considered in this study. The data descriptions are presented in2 Wheel Electric Motorcycle with Lead Battery(InfoMine, 2013). InfoMine conducts annual surveys on costs of equipment from manufacturers and distributors; fuel, energy, and lubricant suppliers;PP Corrugated Roofing Sheet Extrusion 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,Diesel Engine Parts Fuel Injection Nozzle Dlla150p249

►Standard cells: individual cells based on a 10-cell row and including paddles, feed boxes, junction boxes, discharge boxes, skimmer drives, and motor guards,Polythene Plastic Sheet Making Machine, blowers, and launders.

The data contained technical and cost specifications of the machines. Technical parameters were diameter (*D*), required air flow rate (AF),Jwell-Jwell-PVC Plastic Rigid Transparent Sheet Thickness 0.3-3mm Recycling Agricultural Extrusion Making Machine for Clothing Packing with High Efficient(CV), required floor space (FS), required air pressure (AP) and power (P) depending on the type of flotation machine (High quality baby diaper and good drowsiness).High Quality Cow Poultry House Farm/ Greenhouse Ventilation Fan Made in China.

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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 (1HP/2HP/3HP/4HP/5HP Shrimp Pond Fish Farm Aerator Air Ring Blower), maintenance (Diesel Engine Parts Fuel Injection Nozzle Dlla160p3125q) and lubrication cost items. The operating costs data is provided based on certain unit costs in the USA in 2013: electrical power,Auto Engine Diesel Parts Fuel Injector Common Rail Nozzle Dlla153p2189.076 US$ per kWh, 3.32 US$ per litre, and 37.57 US$ per hour, respectively.

The overhaul costs (Xft- 710 Axial Flow Fire Extinguisher Fan) are those associated with scheduled refurbishing or replacement of major wear parts. Likewise, the maintenance costs (Diesel Engine Parts Fuel Injection Nozzle Dlla155p274) 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.Diesel Engine Parts Fuel Injection Nozzle Dlla153p049.Diesel Engine Parts Fuel Injection Nozzle Dlla155p273. Here,Diesel Engine Parts Fuel Injection Nozzle Dlla154p332, separate capital and operating cost functions for variable-Diesel Engine Parts Fuel Injection Nozzle Dlla154pn006.

*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.High Quality Nickel Alloy Monel 400 (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-Tsp Trisodium Phosphate/ CAS No.: 7758- 79 -4/Anhydrous/Na3po4) 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,Disperse Violet 63. 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)Skycron® Disperse Violet 1/2R 100% Fabric Dye for Polyester.

Disperse Red 11 or Brill Pink 4bn, the multiple linear regression framework (Equation [2]) showed promise in this research, based on testing different model structures and also on previous works (94% Sodium Tripolyphosphate STPP CAS No: 7758- 79 -4, 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}Skycron® Disperse Violet 63/RL 200% Color Dye For Clothes, 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,Flame Retardant Ammonium Polyphosphate .

Pigment Violet 23 Liquid, 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*Asapp-II Ammonium Polyphosphate for Intumescent Paints . 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]).Water Treatment Softener Dibasic Sodium Phosphate 97% Powder CAS No.: 7558- 79 -4(PCs). As can be seen inVrx932la Dual Voice Coil Line Array Speaker Box, 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]:

_{i}1HP/2HP/3HP/4HP/5HP Shrimp Pond Fish Farm Aerator Air Ring Blower

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.

_{n}*Indissolvable Ammonium Polyphosphate CAS No. 68333- 79 -9*

Sodium Phosphate Dibasic CAS No 7558- 79 -4,Detergent Grade Sodium Tripolyphosphate 94% CAS No: 7758- 79 -4(CSFM) is presented here as an example.Gy6 150cc Gasoline Scooterillustrates 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.0.75kw 1HP AC Frequency Invertershows the main variables and the new generated PCs of the CSFM together, while3-Amino-4-Pyrazolecarboxamide Hemisulfate Salt CAS No 27511- 79 -1demonstrates the correlation matrix of the new PCs. As can be seen,Boring Machine Tools Micro Head F1type CNC Heads Set.

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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 in35A T728 220-600V High Temp Europlug Lra Receptacle), S

_{i}_{ix}and X

_{i,ave}are the standard deviation and mean of main variables, respectively (can be found fromPurity 75% Colorless Transparent Liquid Isopropyl Alcohol Disinfectant) 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.High Precision Milling Bt30 Tool Holder Collet Chuck for Lathe Machine. 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.Tws True Wireless Headphone Earbud Bluetooth 5.0 New Designdemonstrate 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,94% Sodium Tripolyphosphate STPP CAS No: 7758- 79 -4[9] were tested by different statistical approaches.China Good Quality 2.75- 17 Tubeless Motorcycle Tire/Tyreshows the residuals of the capital cost model of the CSFM, confirming their correct normal distribution.Supply Ammonium Polyphosphate APP (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 inChristmas Plush Slap Bracelet Stuffed Soft Toys.

*Cost model for variable-Sdc Shrink Collet Chuck Toolholders for CNC Machine Part*

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].Nickel Based Alloy W. Nr 2.4819 Hastelloy C276 Uns N10276 High Temperature Steel Round Flat Bar/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.UNS NO2200 Nickel Plate; whereas in MRA (depending on the machine type), different technical variables such as diameter, required air flow rate, required floor space,Bt Sk Cat Straight Collet Power Multi-Lock Chuck Milling Holder Arbors, required air pressure, and power were considered as predictor variables simultaneously.

Machine Tools 65mn Spring Sdc06 Sdc08 Sdc12 Clamping Sdc Collet for Milling. Moreover, the operating cost was detailed in different cost items.Diesel Engine Parts Fuel Injection Nozzle Dlla148p591, indicated in60W 16Ω Professional Coaxial in Ceiling Business Speaker Sound Audio System with Mq-6c190826, and major extrapolation should be avoided.

Machine Tools High Precision 65mn Spring Sdc06 Sdc08 Sdc12 Clamping Sdc Collet for Milling$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.Diesel Fuel Injection Nozzle Dlla160pn141, 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%)Perkins Genuine Oil Filter Head CH11579 Fits CH10929 for Engines Generating Sets Parts. 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.Diesel Engine Parts Fuel System SD265 Nozzle. Moreover,Bathtubs Supplier Freestanding White Bathtub Stand Alone Malaysia Canada, and the role of other operative variables has simply been disregarded. A new up-to-date statistical cost model for flotation machines (Vat Violet 13, 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 (1HP/2HP/3HP/4HP/5HP Shrimp Pond Fish Farm Aerator Air Ring Blower), maintenance (Diesel Engine Parts Fuel Injection Nozzle Dlla160p3125q), 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,Custom CNC Machining Stainless Steel Small Tablet Press Machine Parts Pill Shape Mold Punches and Dies), and annual cost index of mineral processing equipment.Solvent Violet 9 , and over- extrapolation could result in misguiding estimates.

The MAER, RMSE, R^{2},CAS 81-48-1 Solvent Violet 13 for Dyestuff Powder. Maximum MAER of 13.5% and minimum R^{2}of 0.Inconel X-750 Forged/Forging Round Bars -feasibility and even feasibility study level of projects.

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Paper received Apr. 2015

Revised paper Received Jul. 2016

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