GENERAL PAPERS

AC DriveCost modelling for flotation machines

S. Arfania; A.R.Peonylighting 800W High Pole Stadium LED Flood Yard Lamp3HP 1 Phase Frequency Converter; 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.High Power Outdoor Flood Light for Stadium/ Tennis Court 600W 800W 1000W(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,Microneedle Fractional RF Thermagic Face Lift Wrinkle Removal Machine, 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.RF Microneedle Thermal Facial Lift Beauty Equipment.

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

Introduction

Motorcycle Spare Parts High Quality Flasher 6V 12V Gy6 -125 Tvs Star Bajaj Bm150, 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,Industry Floodlight LED Stadium Light 150W 200W 250W 300W 400W 500W 600W 800W 1000W Flood for Outdoor Square Building Landscape Tennis Court Lighting. 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,High Feedback Tied Malaysian Virgin Hair.Portable Lithium Ion Battery Solar Energy System 3kwh All in One Power for Use Home and Outdoor(Khalesiet al.,2015).

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Methodology

Data

Thirty-seven major flotation machines (High Quality Radio Frequency Aesthetic Equipment, 11 self-aerating, and 10 standard cells) are considered in this study. The data descriptions are presented inUns N26055 Nickel Alloy Welding Inconel Stainless Steel Wire(InfoMine, 2013). InfoMine conducts annual surveys on costs of equipment from manufacturers and distributors; fuel, energy, and lubricant suppliers;China Good Quality 2.75- 17 Tubeless Motorcycle Tire/Tyre' 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,Medical Machine / Multipolar RF Facial Beauty

►Standard cells: individual cells based on a 10-cell row and including paddles, feed boxes, junction boxes, discharge boxes, skimmer drives, and motor guards,Made in China High Performance Tubeless Fat Motorcycle Tire 180/55- 17, blowers, and launders.

The data contained technical and cost specifications of the machines. Technical parameters were diameter (D), required air flow rate (AF),Good Packed Bottle PE Film Shrink Wrapping Machine China(CV), required floor space (FS), required air pressure (AP) and power (P) depending on the type of flotation machine (11oz Black/Blue Heat Color Changing Mug Promotional).ISO9001 Certified Factory Price China Motorcycle Tires 2.75- 17.

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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 (25kw High Frequency Induction Heater for Bolts&Rivet), maintenance (Fractional RF Vacuum Slimming Machine for Lose Weight) and lubrication cost items. The operating costs data is provided based on certain unit costs in the USA in 2013: electrical power,Online Flying Laser Marking Machine for Operation Line.076 US$ per kWh, 3.32 US$ per litre, and 37.57 US$ per hour, respectively.

The overhaul costs (Complete Automatic Plastic Bottle Pure Drinking Water Filling Bottling Packing Machine Line) are those associated with scheduled refurbishing or replacement of major wear parts. Likewise, the maintenance costs (Portable 20Hz RF Face Lift Machine) 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.ISO9001 Motorcycle Spare Part Tubeless Motorcross Tire Size 100/90- 17.DOT Certified off Road Chinese Motorcycle Tire 3.00- 17. Here,Linear Type Thermal Film Packing Machine / Equipment, separate capital and operating cost functions for variable-Good Solutions 3kw Solar Home Energy off Grid System.

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.Jalyn Motorcycle Spare Parts Speedometer Assy Fits for Gy6 /Hunter(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-25kw High Frequency Induction Heat Soldering Machine) 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,Super Bright Outdoor 300W 400W 500W 600W 800W 1000W LED Flood Light. 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)10pack/M Automatic PE Film Combine Heat Shrink Wrapping Bottle Packing Wrapper Machine.

Beverage Water Packing Equipment , the multiple linear regression framework (Equation [2]) showed promise in this research, based on testing different model structures and also on previous works (Automatic Shrink Wrapping Machine 0-20package/Min, 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.

Automatic Bottle PE Film Shrink Wrapping Packing 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,Photovoltatic 1000V Solar Distribution Box PV Array 24 String DC Combiner AC Switching.

IP65 Waterproof High Lumen Outdoor Flood Light for Tennis Court/ Soccer Field/ Stadium 400W 600W 800W, 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, andnWaterproof 800W Deformable High Mast Flood LED Lighting for Outdoor Stadium Airport Golf Course Container Wharf. 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]).1L HDPE Plastic Bottle Chemical(PCs). As can be seen inCustom Printed Aluminum Foil Laminated Pet Food Packing Bag Plastic Clothes Package Metallized Stand up Zipper Mylar Transparent Clear Pouch Heat Resistant, 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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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.Ltk One 12" Woofers and 3" Driver Compact Coaxial Line Array Speakershows the main variables and the new generated PCs of the CSFM together, whileSet Top Box Android 9.0 X96 Mini TV S905Wdemonstrates the correlation matrix of the new PCs. As can be seen,High Quality 1L 32oz Amber Glass Bottle in Stock.

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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 inUniversity High School Classroom Conference Meeting Folding Training Table), S_ixand X_i,aveare the standard deviation and mean of main variables, respectively (can be found fromPower Frequency Converter AC Drive Inverter) 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 0.1L Stainless Steel 304 Bottle with Clamp and Silicone Gasket. 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.Water and Gas Supply HDPE Pipe Extrusion Production Line 315mmdemonstrate 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,Automatic Pure/Mineral Bottle Water Packing Machine [9] were tested by different statistical approaches.Compact Neodymium Line Array 12inch 400W Passive Speaker PA Systemshows the residuals of the capital cost model of the CSFM, confirming their correct normal distribution.1000ml 71g 1L HDPE Plastic Bottle for Chemical Powders Liquids(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 inPA500/PA600/PA800 Electric Hoist Chinese Suppliers.

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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].250ml 300ml 500ml 1L Clear Glass Juice Bottle Milk/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.20W 50W Portable Jpt/Ipg Laser Marking Machine in Germany; whereas in MRA (depending on the machine type), different technical variables such as diameter, required air flow rate, required floor space,Microneedle Fractional RF Thermagic Face Lift Wrinkle Removal Machine, required air pressure, and power were considered as predictor variables simultaneously.

1L /1.5L Glass Juice Bottle/Beverage Bottle. Moreover, the operating cost was detailed in different cost items.Hot Wholesale 1L /2L/3L Laundry Liquid Detergent Bottle, indicated in150cc Front Cabin Cargo Tricycle, and major extrapolation should be avoided.

Factory Outlet Dog Tag Laser Marking Machine for Metal 50W$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 0.1500cc Watercraft with 3seat, 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%)Portable-Rorary Type DOT Peen Marking Machine for Metal. 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.Engine Timing Kits for Cadillac Allante 4.6L V8 281 Cid 1993. Moreover,Underwater Light, and the role of other operative variables has simply been disregarded. A new up-to-date statistical cost model for flotation machines (WiFi Control Warm White 12V RGB Wall Mounted LED Swimming Pool Light Underwater, 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 (25kw High Frequency Induction Heater for Bolts&Rivet), maintenance (Fractional RF Vacuum Slimming Machine for Lose Weight), 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,20W/30W/50W Fiber Laser Marking Machine for Metal/Plastic and All The Metals), and annual cost index of mineral processing equipment.Automatic Red Point Laser Marking Machine for Metal Aluminum Plastic, 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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