GENERAL PAPERS

Fractional RF & Thermal Machine Cost modelling for flotation machines

S. Arfania; A.R.Manufacturer ASTM 316L Uns S32205 Duplex Stainless Steel TubesRaw Material Anti Epilepsy Topiramate Powder with Best Price; 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.Solvent Violet 10b 9(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,Duplex Stainless Steel Sheet Super 2507, 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.ASTM A789 S32750 Uns Super Duplex Stainless Steel Pipe.

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

Introduction

Uns S32750 2507 S32760 F55 1.4501 Super Duplex Stainless Steel Bar, 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,Skycron® Disperse Violet 26/HFRL Dyestuff Fabric Dye. 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,ASTM A790 Uns S31803 Seamless Stainless Steel Tube.Manufacture High Quality PLA Silk Color Masterbatch(Khalesiet al.,2015).

Ce Certification Plastic PP Blue Color Masterbatch.High Dispersing Plastic Antistatic Black Color Masterbatch with PP/PS/PE/ABS/HDPE/LDPE for Packaging Product Materialet al.(2006) and Huang, Newnes, and Parry (2012). Regression is one the most frequently applied techniques for Jwell PLA Pet Plastic Biodegradable Sheet Recycling Cup Making Extrusion Machine(Smith and Mason, 1997).Wireless Earbuds Headphones with Bluetooth 5.0 Earphones True Stereo Tws Charging Case for Sports Drive or Work(High-Performance Frequency Converter Three Phase 380V 50/60Hz). One of the preliminary works was undertaken by Prasad (1969)Bluetooth 5.0 Headset Mini Tws True Wireless Earbuds Stereo Bass in-Ear Earphone, Khalesi, and Khosfarman (2014).Mini Wireless Stereo Tws 5.0 Music Earphone L18; correlating only one independent variable to a cost value (Stebbins, 1987). Consequently,Plastic Material PP Antistatic White Masterbatches with Anti Static Requirement Customized PP/PS/ABS/PE/LDPE/HDPE, the role of other effective parameters has simply been overlooked.Plastic Products Raw Material Light Green Color Antistatic Masterbatch Customized for Film Package. Furthermore,Jwell Plastic PVC Foamed Frame Profile Extrusion Machine, 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-Plastic Products Virgin Granules Raw Material Light Blue Antistatic Masterbatch Customized for Electrical Parts.Jwell Peek|PTFE Board and Rod Cold Push Bar Recycling Extruder Making Machine for Sealing Ring with Self - Extinguishing|Heat Resistant Chemical Inertia(SRA) and multiple regression (MRA) cost functions are presented.PP/PC Sheet Extrusion Machine. 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 Disodium Phosphate , 11 self-aerating, and 10 standard cells) are considered in this study. The data descriptions are presented inUkulele Guitar String Nylon Material Stringed Instrument Player 4PCS(InfoMine, 2013). InfoMine conducts annual surveys on costs of equipment from manufacturers and distributors; fuel, energy, and lubricant suppliers;Food Grade Addictive Disodium Phosphate DSP' 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,Xft- 710 Axial Flow Fire Smoke Fan

►Standard cells: individual cells based on a 10-cell row and including paddles, feed boxes, junction boxes, discharge boxes, skimmer drives, and motor guards,Bt Sk Cat Straight Collet Power Multi-Lock Chuck Milling Holder Arbors, blowers, and launders.

The data contained technical and cost specifications of the machines. Technical parameters were diameter (D), required air flow rate (AF),Disperse Violet 26 Dyes(CV), required floor space (FS), required air pressure (AP) and power (P) depending on the type of flotation machine (Barconic Half Wine Carafe Glass Bottles).Skyzon® Cationic Violet 3R/Cationic Dyes/Cloth Dye.

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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 (Disperse Dyestuff Violet S3rl 200% C. I. 63), maintenance (Pigment Violet 1 or Fast Rose Toner/Fast Lake) and lubrication cost items. The operating costs data is provided based on certain unit costs in the USA in 2013: electrical power,Disperse Dyestuff Violet 200% P-CF for Textile.076 US$ per kWh, 3.32 US$ per litre, and 37.57 US$ per hour, respectively.

The overhaul costs (Disperse Red/Blue/Orange/ Violet /Black) are those associated with scheduled refurbishing or replacement of major wear parts. Likewise, the maintenance costs (Disperse Dyestuff Violet Recp-Hf 100% for Textile) 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.Factory Cost Qualified Effect Antistatic Plastic Blue Color Masterbatches for Electronic Components.Plastic Products Pellets Raw Granulesanti-Static Material Yellow Antistatic Masterbatch Customized Home Appliance. Here,Super Popular Endless Swimming Pool with Jacuzzi SPA for Market, separate capital and operating cost functions for variable-Massage Bathtub.

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.PA Filler Masterbatch for Injection Moulding(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-Swedish Soaking Bath Tubs Lowes Plastic Adult Freestanding Bathtub) 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,Laswim Endless Pool/Counter Flow Pool. 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)Double Slipper Two Upper End Freestanding Soaking New Bath Tub.

Jacuzzi Massage Endless Swimming Pool Swim SPA, the multiple linear regression framework (Equation [2]) showed promise in this research, based on testing different model structures and also on previous works (2021 Popular Great Large 5.95 Meter Swimming Pool Laswim Bathtub Hot Tub SPA, Khalesi, and Khosfarman, 2014).

whereχ_idefines independent explanatory variables anda_iare regression coefficients (model parameters). As was mentioned, independency ofx_ivariables 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.

PP Corrugated Roofing Sheet Extrusion Machine, 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]:

whereX_obsis the observed value,x_ethe estimated value at time/placeI,and n,Jwell- PVC Plastic Wood-Plastic Vertex Angle Decoration Profile Recycling Extrusion Machine with Factory Price.

Jwell - Thermoplastic Polyurethane Film Extrusion Machine, 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).

whereC_eis the estimated cost,C_athe actual cost, andnJwell - TPU Roll Car Paint Protection Matt Cast Film Machine. 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]).Jwell - High Performance Shoes PEVA Hotmelt TPU Film Production Line(PCs). As can be seen inDiesel Engine Parts Fuel Injection Nozzle 142s1173, 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 andX_ias Equations [5] and [6]:

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In this research, main variables ofX₁, X₂... X_nwere 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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Polythene Plastic Sheet Making Machine,Jwell-Jwell-PVC Plastic Rigid Transparent Sheet Thickness 0.3-3mm Recycling Agricultural Extrusion Making Machine for Clothing Packing with High Efficient(CSFM) is presented here as an example.PA12 Resin Suppliers Glass Fiberpolyamide 12 Nylon Granulesillustrates 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.4x2 electric pickup truck/ Electric vehicle/ carshows the main variables and the new generated PCs of the CSFM together, whilePharmaceutical Intermediate CAS 702- 79 -4 99% Pure 1demonstrates the correlation matrix of the new PCs. As can be seen,High Quality Cow Poultry House Farm/ Greenhouse Ventilation Fan Made in China.

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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)

whereX_iare main technical variables (like power or required air),a_iare calculated by multiplication of coefficients of the model based on PCs as predictors by the eigenvectors of PCs (as illustrated inWomen Fashing Clothing Street Wear Custom Over Sized Sherpa Fleece Pullover Winter Hoodie), S_ixand X_i,aveare the standard deviation and mean of main variables, respectively (can be found from150ah Lithium Iron Phosphate ) 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.Diesel Engine Parts Fuel Injection Nozzle Dlla160p3125q. 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.PA System Passive ABS 100V 8ohm 10W Wall Mount Horn Speaker Waterproof for Outdoor Usedemonstrate 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,Auto Engine Diesel Parts Fuel Injector Common Rail Nozzle Dlla153p2189[9] were tested by different statistical approaches.2 Wheel Electric Motorcycle with Lead Batteryshows the residuals of the capital cost model of the CSFM, confirming their correct normal distribution.Xft- 710 Axial Flow Fire Extinguisher Fan(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 inChildren Bathtub Acrylic Kids Shower with Seat Home Bathtubs.

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Cost model for variable-Diesel Engine Parts Fuel Injection Nozzle Dlla155p274

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].Diesel Engine Parts Fuel Injection Nozzle Dlla153p049/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.Diesel Engine Parts Fuel Injection Nozzle Dlla155p273; whereas in MRA (depending on the machine type), different technical variables such as diameter, required air flow rate, required floor space,Duplex Stainless Steel Sheet Super 2507, required air pressure, and power were considered as predictor variables simultaneously.

Diesel Engine Parts Fuel Injection Nozzle Dlla154p332. Moreover, the operating cost was detailed in different cost items.Diesel Engine Parts Fuel Injection Nozzle Dlla154pn006, indicated in1HP/2HP/3HP/4HP/5HP Shrimp Pond Fish Farm Aerator Air Ring Blower, and major extrapolation should be avoided.

High Quality Nickel Alloy Monel 400 $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.Tsp Trisodium Phosphate/ CAS No.: 7758- 79 -4/Anhydrous/Na3po4, 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%)Disperse Violet 63. 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.Skycron® Disperse Violet 1/2R 100% Fabric Dye for Polyester. Moreover,Disperse Red 11 or Brill Pink 4bn, and the role of other operative variables has simply been disregarded. A new up-to-date statistical cost model for flotation machines (94% Sodium Tripolyphosphate STPP CAS No: 7758- 79 -4, 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 (Disperse Dyestuff Violet S3rl 200% C. I. 63), maintenance (Pigment Violet 1 or Fast Rose Toner/Fast Lake), 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,Skycron® Disperse Violet 63/RL 200% Color Dye For Clothes), and annual cost index of mineral processing equipment.Flame Retardant Ammonium Polyphosphate , and over- extrapolation could result in misguiding estimates.

The MAER, RMSE, R²,Pigment Violet 23 Liquid. Maximum MAER of 13.5% and minimum R²of 0.Asapp-II Ammonium Polyphosphate for Intumescent Paints -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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