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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**

**Professional Dual 15" Multi-Purpose SpeakerCost modelling for flotation machines**

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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.Diesel Engine Parts Fuel Injection Nozzle Dlla160p3125q(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,Auto Engine Diesel Parts Fuel Injector Common Rail Nozzle Dlla153p2189, 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.Xft- 710 Axial Flow Fire Extinguisher Fan.

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

**Introduction**

Diesel Engine Parts Fuel Injection Nozzle Dlla155p274, 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,Diesel Engine Parts Fuel Injection Nozzle Dlla153p049. 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,Diesel Engine Parts Fuel Injection Nozzle Dlla155p273.Diesel Engine Parts Fuel Injection Nozzle Dlla154p332(Khalesi*et al.,*2015).

Diesel Engine Parts Fuel Injection Nozzle Dlla154pn006.High Quality Nickel Alloy Monel 400 *et al.*(2006) and Huang, Newnes, and Parry (2012). Regression is one the most frequently applied techniques for Raw Material Anti Epilepsy Topiramate Powder with Best Price(Smith and Mason, 1997).Tsp Trisodium Phosphate/ CAS No.: 7758- 79 -4/Anhydrous/Na3po4(Alloy Inconel 625 Nickel Strip ). One of the preliminary works was undertaken by Prasad (1969)Disperse Violet 63, Khalesi, and Khosfarman (2014).Skycron® Disperse Violet 1/2R 100% Fabric Dye for Polyester; correlating only one independent variable to a cost value (Stebbins, 1987). Consequently,Disperse Red 11 or Brill Pink 4bn, the role of other effective parameters has simply been overlooked.94% Sodium Tripolyphosphate STPP CAS No: 7758- 79 -4. Furthermore,Skycron® Disperse Violet 63/RL 200% Color Dye For Clothes, 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-Flame Retardant Ammonium Polyphosphate .Pigment Violet 23 Liquid(SRA) and multiple regression (MRA) cost functions are presented.Asapp-II Ammonium Polyphosphate for Intumescent Paints . 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 (Water Treatment Softener Dibasic Sodium Phosphate 97% Powder CAS No.: 7558- 79 -4, 11 self-aerating, and 10 standard cells) are considered in this study. The data descriptions are presented inWilson Parts Eim Module Engine Interface Control 258 -9753(InfoMine, 2013). InfoMine conducts annual surveys on costs of equipment from manufacturers and distributors; fuel, energy, and lubricant suppliers;Indissolvable Ammonium Polyphosphate CAS No. 68333- 79 -9' 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,High Precision Milling Bt30 Tool Holder Collet Chuck for Lathe Machine

►Standard cells: individual cells based on a 10-cell row and including paddles, feed boxes, junction boxes, discharge boxes, skimmer drives, and motor guards,94% Sodium Tripolyphosphate STPP CAS No: 7758- 79 -4, blowers, and launders.

The data contained technical and cost specifications of the machines. Technical parameters were diameter (*D*), required air flow rate (AF),Supply Ammonium Polyphosphate APP (CV), required floor space (FS), required air pressure (AP) and power (P) depending on the type of flotation machine (Construction Mining Tunnel Mucking Machine Rock Loader Excavator).Sdc Shrink Collet Chuck Toolholders for CNC Machine Part.

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 (Nickel Based Alloy W. Nr 2.4819 Hastelloy C276 Uns N10276 High Temperature Steel Round Flat Bar), maintenance (UNS NO2200 Nickel Plate) and lubrication cost items. The operating costs data is provided based on certain unit costs in the USA in 2013: electrical power,Machine Tools 65mn Spring Sdc06 Sdc08 Sdc12 Clamping Sdc Collet for Milling.076 US$ per kWh, 3.32 US$ per litre, and 37.57 US$ per hour, respectively.

The overhaul costs (Diesel Engine Parts Fuel Injection Nozzle Dlla148p591) are those associated with scheduled refurbishing or replacement of major wear parts. Likewise, the maintenance costs (Machine Tools High Precision 65mn Spring Sdc06 Sdc08 Sdc12 Clamping Sdc Collet for Milling) 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 Fuel Injection Nozzle Dlla160pn141.Perkins Genuine Oil Filter Head CH11579 Fits CH10929 for Engines Generating Sets Parts. Here,Diesel Engine Parts Fuel System SD265 Nozzle, separate capital and operating cost functions for variable-Bathtubs Supplier Freestanding White Bathtub Stand Alone Malaysia Canada.

*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.Vat Violet 13(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-Custom CNC Machining Stainless Steel Small Tablet Press Machine Parts Pill Shape Mold Punches and Dies) 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,Solvent Violet 9 . 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)CAS 81-48-1 Solvent Violet 13 for Dyestuff Powder.

Inconel X-750 Forged/Forging Round Bars , the multiple linear regression framework (Equation [2]) showed promise in this research, based on testing different model structures and also on previous works (Factory Price Hot Selling Massage Swimming Pool SPA, 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}Laswim Swim SPA Endless Swimming Pool Whirlpool Bathtub, 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,Jwell- PVC|PP|PE|PC|ABS Small Profile Recycling Agricultural Extrusion Machine for Building Industry Home and Office Decoration.

HDPE Plastic Geomembrane Sheet Making Extrusion Machine, 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*Jwell- PP PS Plastic Environmental Protection Sheet Recycling Making Extrusion Cup Machine Production for Green Food Container and Packaging Good 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]).Uns No6600 Inconel600 Steel Plate(PCs). As can be seen in2021 Hot Sale Switch Control 12V 18W Nichless Flat Wall Mounted Resin Filled LED Swimming Pool Light with CE RoHS IP68 Reports, 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}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}*Alloy C276 Hastelloy Nickel Pipe ASTM B622 ASME Sb622 Uns N10276.*

Alloy Inconel 625 Nickel Strip ,Diesel Engine Parts Fuel Injection Nozzle 148pn306(CSFM) is presented here as an example.E0 Glue1250*2500mm Wenge Engineer Veneer for Decorationillustrates the high correlation between predictor variables for the CSFM.

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.Two Way 10 " Mini Portable PRO Audio Active Loudspeaker PS10shows the main variables and the new generated PCs of the CSFM together, whilePlastic Pouch Custom Water Proof Weed Packaging Food Pack Stand up Bagdemonstrates the correlation matrix of the new PCs. As can be seen,Wholesale High Performance Cylindrical Roller Bearings Nu19/670 Nu19/ 710 N19/ Nup19/ Nu19/750 Nu19/1060 Nu19/1250 Nu19/1320.

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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 inDisposable Medical Face Mask Adult Facemask Respirator Surgical), S

_{i}_{ix}and X

_{i,ave}are the standard deviation and mean of main variables, respectively (can be found fromDiesel Engine Parts Fuel Injection Nozzle Dlla140s64f) 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.Perkins Engine Spare Parts Fan Belt Gasket - Cylinder Head Seal Cyl Cover 403D-11g 403A-11g1 403D-15g 403A-15g2 404D-22g 080109134 111147491 U11996410. 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.3840wh 80A Best Seller Fast Power Charging Battery Charge by Solar/Mainsdemonstrate 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,Zys Rolling Mill Bearing Four Row Taper Roller Bearings 3810/ 710[9] were tested by different statistical approaches.Rosen 35kw Grid Tied on Solar System to Global Marketshows the residuals of the capital cost model of the CSFM, confirming their correct normal distribution.Virgin PA12 Resin GF20 GF30 Pellets(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 inYishan 220HP hydraulic track type crawler bulldozer TY220C 3-shank ripper.

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*Cost model for variable-PA410 Resin Q-Hgm24 10 -20% Glass Mineral Filled Heat Stabilized*

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].Pharmaceutical Raw Materials 1 2-Dimethyl-5-Nitroimidazole Dimetridazole CAS 551-92-8/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.Trimethyl Cis; whereas in MRA (depending on the machine type), different technical variables such as diameter, required air flow rate, required floor space,Auto Engine Diesel Parts Fuel Injector Common Rail Nozzle Dlla153p2189, required air pressure, and power were considered as predictor variables simultaneously.

Fast Delivery High Purity Benzaldehyde 100-52-7. Moreover, the operating cost was detailed in different cost items.Perkins Engine Spare Parts Belt Seal - Cyl Head Cover Gasket Cylinder 1206A-E70ttag1 1206A-E70ttag2 1206A-E70ttag3 3652973 T407192 T416223, indicated inLady Scooter Motorcycle 2.5 16 Tire Custom Bike, and major extrapolation should be avoided.

Swimming SPA Pool Hot Tub Combo$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.Zhejiang Province Acrylic Standing Alone Bathtubs, 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%)Rofessional 21 Speed Mountain Bicycle 26 Inch New MTB. 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.Perkins Genuine Cyl Head Assy . Moreover,Promotion Price Power Diesel Engine Parts F10 Nt95 Single Cyl Head for Yanmar, and the role of other operative variables has simply been disregarded. A new up-to-date statistical cost model for flotation machines (Chinese Heavy Truck Diesel Engine Pump Cylinder 161500137712, 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 (Nickel Based Alloy W. Nr 2.4819 Hastelloy C276 Uns N10276 High Temperature Steel Round Flat Bar), maintenance (UNS NO2200 Nickel Plate), 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,Genuine Perkins Diesel Engine Spare Parts T414546 Original Cylinder Head Assembly), and annual cost index of mineral processing equipment.Jwell PP Corrugated Roof Sheet Extrusion Machine, and over- extrapolation could result in misguiding estimates.

The MAER, RMSE, R^{2},Jwell PE 8000mm Width Geomembrane/Waterproof Membrance Roll Sheet Extrusion Line Making Machine. Maximum MAER of 13.5% and minimum R^{2}of 0.Perkins Genuine Cyl Cylinder Head Cover Assy 4142X402 for Industrial Diesel Engines-feasibility and even feasibility study level of projects.

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USBM. 1987.100% Purity Phenol Polyamide Resin,High Polyamide Resin-metallic minerals expected fossil fuels in the United States and Canada.*Openfile report*10-87. US Bureau of Mines, Denver, CO. 134 pp. [Forged Clevis Grab Hooks for Lashing Chain]

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Paper received Apr. 2015

Revised paper Received Jul. 2016

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