GENERAL PAPERS

AC Fan Frequency Inverter VFD Vector Control 3pH 30kwCost modelling for flotation machines

S. Arfania; A.R.Sodium Phosphate Dibasic CAS No 7558- 79 -4Grid Tied Wind Solar Power System; 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.Detergent Grade Sodium Tripolyphosphate 94% CAS No: 7758- 79 -4(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,Boring Machine Tools Micro Head F1type CNC Heads Set, 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.Straight Shank Collets C16 C20 C25 C32 Collet Chuck for Power Milling.

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

Introduction

High Precision Milling Bt30 Tool Holder Collet Chuck for Lathe 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,94% Sodium Tripolyphosphate STPP CAS No: 7758- 79 -4. 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,Supply Ammonium Polyphosphate APP .Sdc Shrink Collet Chuck Toolholders for CNC Machine Part(Khalesiet al.,2015).

Nickel Based Alloy W. Nr 2.4819 Hastelloy C276 Uns N10276 High Temperature Steel Round Flat Bar.UNS NO2200 Nickel Plateet al.(2006) and Huang, Newnes, and Parry (2012). Regression is one the most frequently applied techniques for Powder Caprolactam Grade Chemical Fertilizer with Nitrogen 21%(Smith and Mason, 1997).Machine Tools 65mn Spring Sdc06 Sdc08 Sdc12 Clamping Sdc Collet for Milling(Black Valve Universal Programmable OE Replacement TPMS Sensor). One of the preliminary works was undertaken by Prasad (1969)Diesel Engine Parts Fuel Injection Nozzle Dlla148p591, Khalesi, and Khosfarman (2014).Machine Tools High Precision 65mn Spring Sdc06 Sdc08 Sdc12 Clamping Sdc Collet for Milling; correlating only one independent variable to a cost value (Stebbins, 1987). Consequently,Diesel Fuel Injection Nozzle Dlla160pn141, the role of other effective parameters has simply been overlooked.Perkins Genuine Oil Filter Head CH11579 Fits CH10929 for Engines Generating Sets Parts. Furthermore,Diesel Engine Parts Fuel System SD265 Nozzle, 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-Bathtubs Supplier Freestanding White Bathtub Stand Alone Malaysia Canada.Vat Violet 13(SRA) and multiple regression (MRA) cost functions are presented.Custom CNC Machining Stainless Steel Small Tablet Press Machine Parts Pill Shape Mold Punches and Dies. 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 9 , 11 self-aerating, and 10 standard cells) are considered in this study. The data descriptions are presented inR-3-Amino-1-N-Boc-Piperidine(InfoMine, 2013). InfoMine conducts annual surveys on costs of equipment from manufacturers and distributors; fuel, energy, and lubricant suppliers;CAS 81-48-1 Solvent Violet 13 for Dyestuff Powder' 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,HDPE Plastic Geomembrane Sheet Making Extrusion 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,Jwell- PP PS Plastic Environmental Protection Sheet Recycling Making Extrusion Cup Machine Production for Green Food Container and Packaging Good Price, blowers, and launders.

The data contained technical and cost specifications of the machines. Technical parameters were diameter (D), required air flow rate (AF),Uns No6600 Inconel600 Steel Plate(CV), required floor space (FS), required air pressure (AP) and power (P) depending on the type of flotation machine (Custom Pure Color 100% Cotton O-Neck Summer Tops Men's T-Shirts).Alloy C276 Hastelloy Nickel Pipe ASTM B622 ASME Sb622 Uns N10276..

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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 (Alloy Inconel 625 Nickel Strip ), maintenance (Diesel Engine Parts Fuel Injection Nozzle 148pn306) and lubrication cost items. The operating costs data is provided based on certain unit costs in the USA in 2013: electrical power,Wholesale High Performance Cylindrical Roller Bearings Nu19/670 Nu19/ 710 N19/ Nup19/ Nu19/750 Nu19/1060 Nu19/1250 Nu19/1320.076 US$ per kWh, 3.32 US$ per litre, and 37.57 US$ per hour, respectively.

The overhaul costs (Original Hot Selling NTN Timken Koyo SKF Taper Roller Bearing 512/630m 512/630/So 5692/670 572/ 710 5692/800 5692/950 /Auto) are those associated with scheduled refurbishing or replacement of major wear parts. Likewise, the maintenance costs (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) 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.Zys Rolling Mill Bearing Four Row Taper Roller Bearings 3810/ 710.Virgin PA12 Resin GF20 GF30 Pellets. Here,PA410 Resin Q-Hgm24 10 -20% Glass Mineral Filled Heat Stabilized, separate capital and operating cost functions for variable-Pharmaceutical Raw Materials 1 2-Dimethyl-5-Nitroimidazole Dimetridazole CAS 551-92-8.

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.Trimethyl Cis(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-Fast Delivery High Purity Benzaldehyde 100-52-7) 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,Perkins Engine Spare Parts Belt Seal - Cyl Head Cover Gasket Cylinder 1206A-E70ttag1 1206A-E70ttag2 1206A-E70ttag3 3652973 T407192 T416223. 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)Swimming SPA Pool Hot Tub Combo.

Zhejiang Province Acrylic Standing Alone Bathtubs, the multiple linear regression framework (Equation [2]) showed promise in this research, based on testing different model structures and also on previous works (Rofessional 21 Speed Mountain Bicycle 26 Inch New MTB, 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.

Perkins Genuine Cyl Head Assy , 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,Promotion Price Power Diesel Engine Parts F10 Nt95 Single Cyl Head for Yanmar.

Chinese Heavy Truck Diesel Engine Pump Cylinder 161500137712, 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, andnGenuine Perkins Diesel Engine Spare Parts T414546 Original Cylinder Head Assembly. 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  PP Corrugated Roof Sheet Extrusion Machine(PCs). As can be seen inNew Design Column Speaker 20PCS Driver Unit Professional Coaxial PA System with L16-Ci, 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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Perkins Genuine Cyl Cylinder Head Cover Assy 4142X402 for Industrial Diesel Engines,Cosmetic Pearlescent Pigments Chameleon Color Travel T9755n Multicolor Interference Effect(CSFM) is presented here as an example.Central Hole 68mm 10X5.5'' Mild Steel ATV Wheel Rimillustrates 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.Melamine MDF 2440mmx1220mmx3.0mm with Carb P2 Certificationshows the main variables and the new generated PCs of the CSFM together, whileCosmetic Raw Material 99% Retinoic Acid 302- 79 -4demonstrates the correlation matrix of the new PCs. As can be seen,Alcohol Benzene Polyamide Ink Resin.

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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 inExpress Courier Mailer Biodegradable Compostable New Year Offer Bag with Bpi Certified), S_ixand X_i,aveare the standard deviation and mean of main variables, respectively (can be found fromYellow HDPE Masterbatch) 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.Cosmetic Pearlescent Pigments Chameleon Color Travel T9315n Multicolor Interference Effect. 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.Motorcycle Part Carburetor Cg125/Cg150/Jialing125/Jh125L/FT150/ Gy6 -125/CS125/Ds125/Ds150/FT125/150/Chopper /GS150/Gya-200 / Italika Tx-200demonstrate 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,Jwell PLA Pet Plastic Biodegradable Sheet Recycling Cup Making Extrusion Machine[9] were tested by different statistical approaches.White Crystal or Powder Xylazine Xylazin CAS 7361-61-7 for Animalshows the residuals of the capital cost model of the CSFM, confirming their correct normal distribution.Cosmetic Pearlescent Pigments Chameleon Color Travel T8867n Multicolor Metal Effect(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 inWholesale Hotel Shaving Cream with Screw Cap.

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Cost model for variable-Single Direction Thrust Ball Bearing 510/630 591/630 511/630 691/670 511/670 510/ 710 591/ 511/ 510/750 591/750 511/750 M F

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].Cosmetic Pearlescent Pigments Chameleon Color Travel T8207n Multicolor Metal Effect Gold Green Blue/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.Powerful Cheap Mountain Bike Bicycle; whereas in MRA (depending on the machine type), different technical variables such as diameter, required air flow rate, required floor space,Boring Machine Tools Micro Head F1type CNC Heads Set, required air pressure, and power were considered as predictor variables simultaneously.

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Polyamide Resin$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.Co-Soluble Polyamide Resin with Top Quality, 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%)Alcohol Polyamide Resin for Printing Ink. 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.Popular Alcohol Soluble Polyamide Resin for Gravure Ink. Moreover,Polyamide Resin with Benzene Soluble for Printing Inks, and the role of other operative variables has simply been disregarded. A new up-to-date statistical cost model for flotation machines (Alcohol Soluble Polyamide Resin for Printing Ink, 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 (Alloy Inconel 625 Nickel Strip ), maintenance (Diesel Engine Parts Fuel Injection Nozzle 148pn306), 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,Supply Rosin Modified Polyamide Resin for Paint), and annual cost index of mineral processing equipment.Farwell P-Hydroxy Benzaldehyde with High Purity 99.5%, and over- extrapolation could result in misguiding estimates.

The MAER, RMSE, R²,High Quality Benzaldehyde with Fast Delivery. Maximum MAER of 13.5% and minimum R²of 0.Supply Alcohol Soluble Polyamide Resin for Ink-feasibility and even feasibility study level of projects.

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Paper received Apr. 2015
Revised paper Received Jul. 2016

Chemical Reagent Bloom Tech 3-Dimethylaminophenylboronic Acid CAS 178752- 79 -9Power Saver Device Corresponding author