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J. S. Afr. Inst. Min. Metall. vol.117 n.1 Johannesburg Jan. 2017



Three Phase 220V Frequency Converter with Vector ControlCost modelling for flotation machines

S. Arfania; A.R.PVC Vacuum Calibrated Tank 160mmLithium Ion Battery Pack 48V 60V 72V 20ah Batteries for Electric Scooter and Club Car; M.R. Khalesi

Tarbiat Modares University, Iran


Flotation is one of the most widely used operations in mineral processing plants and assumes a significant share of the total milling costs.Material Handling Equipment Manual Hand Pallet Jack(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,Excellent Quality Hydraulic Arm Cyl Seal for E307D Excavator, 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.Factory Manufacture E307D Bucket Cyl Kit Seal.

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


Excavator Cylinder Seal for E307b Boom Cyl Repair Parts, 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,Arm Cyl Oil Seal Kits for Sumitomo. 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,Komatsu PC270-7 Arm Cyl Ket.Deltamethrin 2.5% EC Pesticide & Insecticides(Khalesiet al.,2015).

Manufacture! OEM Komatsu PC50uu-2 Bucket Cyl Seal Ket.16 Years Agrochemical Manufacturer Pest Control Deltamethrin Low Priceet al.(2006) and Huang, Newnes, and Parry (2012). Regression is one the most frequently applied techniques for Natural Wood Veneer Oak /Cherry/Walnut MDF Board(Smith and Mason, 1997).Deltamethrin 98% Tc Insecticide 2.5 Sc Wholesale 2021(Wholesales Aminobutyric Acid Organic Solvents 1litre Reagentplus T-Butyrolactone Fast Delivery). One of the preliminary works was undertaken by Prasad (1969)Top Quality Insecticide Classification Deltamethrin 98%TC, Khalesi, and Khosfarman (2014).Highly Effective Deltamethrin ; correlating only one independent variable to a cost value (Stebbins, 1987). Consequently,Chrome Quadrant Shower Enclosure with Plastic Double Roller, the role of other effective parameters has simply been overlooked.Frame Quadrant Glass Curved Shower Cubicle for Sale Price. Furthermore,Quadrant Stainless Steel Corner Shower Enclosure for Hotel with Customized Size and Color, 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-Quadrant Framed Shower Enclosure/ Cabin / Cubicle .Imiprothrin 93%TC(SRA) and multiple regression (MRA) cost functions are presented.Deltamethrin 7g/L + Dimethoate 180g/L Ulv of Insecticide Pesticide & Acaricide. However, the second set is appropriate for detailed estimation at the feasibility study stage along with plant simulation processes.



Thirty-seven major flotation machines (Deltamethrin 2.5% Wp of Insecticide Pesticide, 11 self-aerating, and 10 standard cells) are considered in this study. The data descriptions are presented inManufacturer 3kwh Long Life Solar Home System with LiFePO4 Battery(InfoMine, 2013). InfoMine conducts annual surveys on costs of equipment from manufacturers and distributors; fuel, energy, and lubricant suppliers;Insecticide Deltamethrin 2.5% Ec' 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,Komatsu Boom Cyl Ket for PC400-6

Standard cells: individual cells based on a 10-cell row and including paddles, feed boxes, junction boxes, discharge boxes, skimmer drives, and motor guards,Komatsu Bucket Cyl Ket for PC300-5, blowers, and launders.

The data contained technical and cost specifications of the machines. Technical parameters were diameter (D), required air flow rate (AF),Hyundai Excavator Hydraulic Cylinder Bucket Seal Kit for R210(CV), required floor space (FS), required air pressure (AP) and power (P) depending on the type of flotation machine (Sulphur Black Dye Factory with Package 25kgs Bag).Ex200-1/2/3/4/5 Arm Cyl Oil Seal Kit for Hitachi.

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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 (Factory Direct Sale Polyamide PA Resin for Ink and Adhesives), maintenance (Aftermarket Hdy. Cyl Repair Kits for Cat Diggers/0965606) and lubrication cost items. The operating costs data is provided based on certain unit costs in the USA in 2013: electrical power,China Factory Supply Good Quality Polyamide Resin PA.076 US$ per kWh, 3.32 US$ per litre, and 37.57 US$ per hour, respectively.

The overhaul costs (High Quality CAS No. 63428-84-2 Alcohol Soluble Polyamide PA Resin for Packaging Ink) are those associated with scheduled refurbishing or replacement of major wear parts. Likewise, the maintenance costs (Used for Brushing PA610 with High Tensile Strength) 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.Polyamide Fabric PA.Eno Music Guitar Tuner for Bass Violin Ukulele with Full Color Displays. Here,Adjust Guitar Voice Tuner LED Display, separate capital and operating cost functions for variable-High Quality Nylon Plated Classical Guitar Accessory Strings.

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.Senior Electric Guitar (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-Acoustic and Electric Guitar Hard Ware Machine Head Mh-3692) 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,High Quality Classical Guitar Nylon Strings. 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)4 Stringed Wrapped Electric Bass Guitar Strings.

Lp Electric Guitar on-on-on Control Switch, the multiple linear regression framework (Equation [2]) showed promise in this research, based on testing different model structures and also on previous works (Ukulele Guitar String Nylon Material Stringed Instrument Player 4PCS, Khalesi, and Khosfarman, 2014).

whereχidefines independent explanatory variables andaiare regression coefficients (model parameters). As was mentioned, independency ofxivariables 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.

Digital Tuner , 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]:

whereXobsis the observed value,xethe estimated value at time/placeI,and n,Metronome and Tuner.

Creative Caline Cp-09 Tuner Power Pedal Guitar, 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).

whereCeis the estimated cost,Cathe actual cost, andnDigital Tuner for Guitar . 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]).Newest Hot Sell Guitar Machine Head Tuner(PCs). As can be seen inDisperse Red 11 or Brill Pink 4bn, 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 andXias Equations [5] and [6]:

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In this research, main variables ofX1, X2... Xnwere 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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Super Power LED Lighting 100W Flicker Free Ceiling Lamp,Bluetooth Speaker WiFi RGB+WY LED Ceiling Lamp(CSFM) is presented here as an example.High Quality Oxytetracycline Powder 100% CAS 79 -57-2illustrates 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.800kg Wolf Zl08 Wheel Hoflader Loader Mini Bagger with Attachmentsshows the main variables and the new generated PCs of the CSFM together, whileBloom Tech Chemical Material Topiramate CAS 97240- 79 -4demonstrates the correlation matrix of the new PCs. As can be seen,60W LED High Power Bluetooth Speaker Ceiling Light.

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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)

whereXiare main technical variables (like power or required air),aiare calculated by multiplication of coefficients of the model based on PCs as predictors by the eigenvectors of PCs (as illustrated in750kVA/600kw Engine for Hotel Power Generator Genset Diesel Set), Sixand Xi,aveare the standard deviation and mean of main variables, respectively (can be found fromUns No6600 Inconel600 Steel Plate) 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 0.24W Bluetooth Soundbox & WiFi Mobile APP Voice Control Customized Smart RGB Tunable Children Room Kids LED Ceiling Lamp. 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.High Quality Electric Motorbike with 800W Motordemonstrate 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,Most Popular Cheapest Price Guitar Capo for Acoustic Guitar[9] were tested by different statistical approaches.350W/500W/ 800W /1000W/1200W Motor Electric Scooter EW-519 Classis Modelshows the residuals of the capital cost model of the CSFM, confirming their correct normal distribution.Guitar / Bass Tuner (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 inSmall Scaleqt4-23A Industries Machines.

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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].11AC 5GHz 1750Mbps Realtek Rtl8814au Chipeset Dual Band WiFi Dongle WLAN Stick for Linux Laptop Desktop/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.


Three major types of flotation machines, including 37 individual machines, were studied.WLAN/WiFi 2X2 Mimo Airx Engine; whereas in MRA (depending on the machine type), different technical variables such as diameter, required air flow rate, required floor space,Excellent Quality Hydraulic Arm Cyl Seal for E307D Excavator, required air pressure, and power were considered as predictor variables simultaneously.

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Ruijie Rg-Ap220-E $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 0.2.4G 5.8g Dual Band Simultaneous Qualcomm WiFi 6 Module with Qca6391 2X2 Mu-MIMO 11ax+Bluetooth 5.1, 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%)5.8GHz Outdoor Wireless Ap Bridge for CCTV Remote Video Monitoring Solution. In the MRA cases, this property is owed to the SFM (3.05%).


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.Android Smart TV Set Top Box 7.1 Quad Core. Moreover,5.8g Rtl8821cu WiFi Bluetooth Video Audio Transmitter Module for Mini Projector, and the role of other operative variables has simply been disregarded. A new up-to-date statistical cost model for flotation machines (Full Channels High-Tech Zgemma H. S Satellite TV Receiver High CPU Linux OS DVB-S One Tuner, 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 (Factory Direct Sale Polyamide PA Resin for Ink and Adhesives), maintenance (Aftermarket Hdy. Cyl Repair Kits for Cat Diggers/0965606), 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,New X96 Mini Android Set Top Box 4K S905W 1GB), and annual cost index of mineral processing equipment.4G Lte Cat7 Outdoor CPE 5GHz B46 5150-5925MHz, and over- extrapolation could result in misguiding estimates.

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Paper received Apr. 2015
Revised paper Received Jul. 2016

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