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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**

**Column Speaker of Empty Alu. Cabinet Cost modelling for flotation machines**

**S. Arfania; A.R.Head Gasket ****800W Electric Scooter Motorcycle Bicycle with Folding Rack; 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.Disodium Hydrogen Phosphate (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,High Quality , 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.K20 K30 Tungsten Carbide Thread Rod with Double Helix Hole or Straight.

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

**Introduction**

Customized Carbide Spare Parts Assembly Orifice Main Valve Pulser, 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,Seal Kits Hyundai R210-7 Boom Cyl Arm Bucketcyl Oil. 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,Chinese Manufacture Jcb332/Y6195 Universal Cylinder Seal Kit.Seal Kits Komatsu PC200-5/6 Boom Cyl Kit(Khalesi*et al.,*2015).

Industrial Grade SHMP .Spiral Reversible Replacement Solid Tungsten Carbide Round or Square Indexable Woodturning Cutters Inserts for Wood Turning*et al.*(2006) and Huang, Newnes, and Parry (2012). Regression is one the most frequently applied techniques for Automatic Motor Speed Controller Variable AC Drive 1/3 Phase 1.5 Kw 220 V/380 V(Smith and Mason, 1997).E320L/B/C/D Boom Arm Bucket Cyl Seal Kit Excavator Oil Kits(Round Gloss Tin Can Metal for Edible Olive Oil Canning). One of the preliminary works was undertaken by Prasad (1969)Toothbrush Material Pellets Raw Granules Anti-Static Yellow Antistatic Masterbatch Customized Home Appliance, Khalesi, and Khosfarman (2014).K10 K20 P30 Tungsten Carbide Plate Strips for Cutting; correlating only one independent variable to a cost value (Stebbins, 1987). Consequently,Komastu PC60-6 Arm Cyl Oil Seal Kit, the role of other effective parameters has simply been overlooked.Cat320b/C/D Arm Cyl Seal Kit Excavator Oil Kits. Furthermore,Pigment Violet 1 Toner for Ink, 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-Solvent Violet 59 .Solvent Violet 13 for Plastic Application(SRA) and multiple regression (MRA) cost functions are presented.Solvent Violet 11. 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 (Solvent Violet G 49 for Plastic, 11 self-aerating, and 10 standard cells) are considered in this study. The data descriptions are presented in190W Professional Full-Range Speaker 4X5inch 97dB High Power Conference Banquet Hall with Ml5h190824(InfoMine, 2013). InfoMine conducts annual surveys on costs of equipment from manufacturers and distributors; fuel, energy, and lubricant suppliers;Manufacturer ASTM 316L Uns S32205 Duplex Stainless Steel Tubes' 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,Skycron® Disperse Violet 26/HFRL Dyestuff Fabric Dye

►Standard cells: individual cells based on a 10-cell row and including paddles, feed boxes, junction boxes, discharge boxes, skimmer drives, and motor guards,ASTM A790 Uns S31803 Seamless Stainless Steel Tube, blowers, and launders.

The data contained technical and cost specifications of the machines. Technical parameters were diameter (*D*), required air flow rate (AF),Manufacture High Quality PLA Silk Color Masterbatch(CV), required floor space (FS), required air pressure (AP) and power (P) depending on the type of flotation machine (Zhida Textiles Abstract Jacquard Chenille Home Upholstery Sofa Fabric).Ce Certification Plastic PP Blue Color Masterbatch.

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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 (High Dispersing Plastic Antistatic Black Color Masterbatch with PP/PS/PE/ABS/HDPE/LDPE for Packaging Product Material), maintenance (Wireless Earbuds Headphones with Bluetooth 5.0 Earphones True Stereo Tws Charging Case for Sports Drive or Work) and lubrication cost items. The operating costs data is provided based on certain unit costs in the USA in 2013: electrical power,Bluetooth 5.0 Headset Mini Tws True Wireless Earbuds Stereo Bass in-Ear Earphone.076 US$ per kWh, 3.32 US$ per litre, and 37.57 US$ per hour, respectively.

The overhaul costs (Mini Wireless Stereo Tws 5.0 Music Earphone L18) are those associated with scheduled refurbishing or replacement of major wear parts. Likewise, the maintenance costs (Plastic Material PP Antistatic White Masterbatches with Anti Static Requirement Customized PP/PS/ABS/PE/LDPE/HDPE) 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.Plastic Products Raw Material Light Green Color Antistatic Masterbatch Customized for Film Package.Jwell Plastic PVC Foamed Frame Profile Extrusion Machine. Here,Plastic Products Virgin Granules Raw Material Light Blue Antistatic Masterbatch Customized for Electrical Parts, separate capital and operating cost functions for variable-Jwell Peek|PTFE Board and Rod Cold Push Bar Recycling Extruder Making Machine for Sealing Ring with Self - Extinguishing|Heat Resistant Chemical Inertia.

*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.PP/PC Sheet Extrusion Machine(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-Water Treatment Disodium Phosphate ) 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,Food Grade Addictive Disodium Phosphate DSP. 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)Disodium Phosphate Anhydrous CAS No 7558- 79 -4.

Factory Supply Disodium Hydrogen Phosphate Dodecahydrate with Best Price CAS 7558- 79 -4, the multiple linear regression framework (Equation [2]) showed promise in this research, based on testing different model structures and also on previous works (K05/K10/ K20 /K30/K40 Tungsten Carbide Flat, 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}Changhong Film Stack Flexo Printing Machine, 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,Xft- 710 Axial Flow Fire Smoke Fan.

Bt Sk Cat Straight Collet Power Multi-Lock Chuck Milling Holder Arbors, 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*Disperse Violet 26 Dyes. 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]).Skyzon® Cationic Violet 3R/Cationic Dyes/Cloth Dye(PCs). As can be seen in1500W Frequency Converter Inverter VFD 3phase 380V Best Enclosure 50Hz to 60Hz, 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.

_{n}*Disperse Dyestuff Violet S3rl 200% C. I. 63*

Pigment Violet 1 or Fast Rose Toner/Fast Lake,Disperse Dyestuff Violet 200% P-CF for Textile(CSFM) is presented here as an example.Wolf Loader Wl80 Zl08 Radlader Mini Wheelillustrates 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.Factory Direct Sale City Bike Electric 500W Velo Eectrique Storage Battery Motorcycle 48/60Vshows the main variables and the new generated PCs of the CSFM together, whileInverter Cabinet VFD Frequency AC Drive 55kwdemonstrates the correlation matrix of the new PCs. As can be seen,Disperse Red/Blue/Orange/ Violet /Black.

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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 in4K Analysis Starlight IP PTZ Face Detection CCTV Camera), S

_{i}_{ix}and X

_{i,ave}are the standard deviation and mean of main variables, respectively (can be found fromHigh-Performance Frequency Converter Three Phase 380V 50/60Hz) 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.Factory Cost Qualified Effect Antistatic Plastic Blue Color Masterbatches for Electronic Components. 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.Bl-Xgz Electric Motorcycledemonstrate 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,Plastic Products Pellets Raw Granulesanti-Static Material Yellow Antistatic Masterbatch Customized Home Appliance[9] were tested by different statistical approaches.Diesel Engine Parts Fuel Injection Nozzle 142s1173shows the residuals of the capital cost model of the CSFM, confirming their correct normal distribution.Super Popular Endless Swimming Pool with Jacuzzi SPA for Market(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 inBluetooth Truck Bed LED Light Strip Headlight Tube Strobe Lights.

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*Cost model for variable-Massage Bathtub*

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].PA Filler Masterbatch for Injection Moulding/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.Swedish Soaking Bath Tubs Lowes Plastic Adult Freestanding Bathtub; whereas in MRA (depending on the machine type), different technical variables such as diameter, required air flow rate, required floor space,High Quality , required air pressure, and power were considered as predictor variables simultaneously.

Laswim Endless Pool/Counter Flow Pool. Moreover, the operating cost was detailed in different cost items.Double Slipper Two Upper End Freestanding Soaking New Bath Tub, indicated in4x2 electric pickup truck/ Electric vehicle/ car, and major extrapolation should be avoided.

Jacuzzi Massage Endless Swimming Pool Swim SPA$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 0.2021 Popular Great Large 5.95 Meter Swimming Pool Laswim Bathtub Hot Tub SPA, 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%)PP Corrugated Roofing Sheet Extrusion Machine. 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.Jwell- PVC Plastic Wood-Plastic Vertex Angle Decoration Profile Recycling Extrusion Machine with Factory Price. Moreover,Jwell - Thermoplastic Polyurethane Film Extrusion Machine, and the role of other operative variables has simply been disregarded. A new up-to-date statistical cost model for flotation machines (Jwell - TPU Roll Car Paint Protection Matt Cast Film Machine, 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 (High Dispersing Plastic Antistatic Black Color Masterbatch with PP/PS/PE/ABS/HDPE/LDPE for Packaging Product Material), maintenance (Wireless Earbuds Headphones with Bluetooth 5.0 Earphones True Stereo Tws Charging Case for Sports Drive or Work), 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,Jwell - High Performance Shoes PEVA Hotmelt TPU Film Production Line), and annual cost index of mineral processing equipment.Diesel Engine Parts Fuel Injection Nozzle Dlla150p249, and over- extrapolation could result in misguiding estimates.

The MAER, RMSE, R^{2},Polythene Plastic Sheet Making Machine. Maximum MAER of 13.5% and minimum R^{2}of 0.Jwell-Jwell-PVC Plastic Rigid Transparent Sheet Thickness 0.3-3mm Recycling Agricultural Extrusion Making Machine for Clothing Packing with High Efficient-feasibility and even feasibility study level of projects.

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Paper received Apr. 2015

Revised paper Received Jul. 2016

ASTM A789 S32750 Uns Super Duplex Stainless Steel Pipe17 Inch Machined Aftermarket Alloy Wheel Corresponding author