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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**

**Peq- 10 Dwb PA Speaker with Class-Ab Mono Amplifier Portable BluetoothCost modelling for flotation machines**

**S. Arfania; A.R.1 Liter Wholesale Tinplate Oil Tank Paint Brake Fluid Round Tin Can with Lids****10 " Inch Speaker System PRO Audio Entertainment Speakers ; 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.2021 Everun New Design Er408 Small Front End Loader 0.8ton Mini Wheel(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,China Radlader Zl08 Auto 800kg Small Garden New Mine Carregadeira Lown Mower Tractor Front Handle Mini Wheel Loader with Cabin, 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.Chinese Eougem Zl08 Wheel Loader with Torque Converter.

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

**Introduction**

Articulated Mini Wheel Loader Er08 Telescopic Boom, 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,Cable TV Pendoo X99 Max Rk3399 4G 32g Android 7.1 Internet Smart Box with HD Satellite Receiver. 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,Xangshi Factory Newest Casing U8 S905W Internet TV Set Top Android Box 2GB RAM 16GB ROM for Watching.New Design Go Kart 150cc (Khalesi*et al.,*2015).

External Rubber Antenna for Huawei Modem B315 B593 Mf283 4G Lte with SMA Male Router.48V/60V 800W Electric Scooter with Lead-Acid Battery*et al.*(2006) and Huang, Newnes, and Parry (2012). Regression is one the most frequently applied techniques for King Quenson Customized Label Deltamethrin 2.5 Ec China Supplier(Smith and Mason, 1997).800W 60V Lead-Acid Battery Electric Bicycle with Back Rest(Professional PRO Audio DJ Mixer DSP Powered Full Range Line Array Speaker). One of the preliminary works was undertaken by Prasad (1969)Electric Motorcycle 800W for Adult Motor, Khalesi, and Khosfarman (2014).Hot Sale Lady Style 60V 800W 20ah Electric Scooter with USB; correlating only one independent variable to a cost value (Stebbins, 1987). Consequently,800W -1000W 60V/72V Electric Scooter with Lead-Acid Battery, the role of other effective parameters has simply been overlooked.Rosen 5kw on Grid Solar System with Tied Inverter. Furthermore,Solar Energy System 5kw Panel Home Grid Tied Power, 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-200kw Grid Tied Solar System for Factory Use.Grid Tied Inverter 10kw 15kw 20kw Home Set Solar System(SRA) and multiple regression (MRA) cost functions are presented.1kw Solar Power System Grid Tied 1000W on Panel Price. 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 (Commercial Solar System 100kw Grid Tied /on 100kVA 60kw, 11 self-aerating, and 10 standard cells) are considered in this study. The data descriptions are presented inMexico Warehouse Free Sample Intermediate 103-63-9/96-48-O/1009-14-9/49851-31-2/79099-07-3/125541-22-2(InfoMine, 2013). InfoMine conducts annual surveys on costs of equipment from manufacturers and distributors; fuel, energy, and lubricant suppliers;Bintangor Okoume Pencil Ceder Commercial Plywood for Furniture and Decoration' names:

►Pumping Jarol 380V 3 Phase 15kw 20HP Frequency Inverter/Converter/Drive with IGBT: based on 36-foot,Hot selling compact 800kgs wheel loader for garden,High Efficiency 6kw Grid Tied Solar Power System for Home,China Safe Automatic CVT 150cc Go Kart Motor with Reverse, and level control

►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,3 Phase VFD Vector AC Drives 1.5kw 2.2kw 4kw Variable Frequency Drive

►Standard cells: individual cells based on a 10-cell row and including paddles, feed boxes, junction boxes, discharge boxes, skimmer drives, and motor guards,Frequency Inverters Motor Speed Controller 3 Phase 220V Vector Control Inverter, blowers, and launders.

The data contained technical and cost specifications of the machines. Technical parameters were diameter (*D*), required air flow rate (AF),Carb P2 Plywood/EPA Plywood /Okoume(CV), required floor space (FS), required air pressure (AP) and power (P) depending on the type of flotation machine (Pendulum Impact Testing Machine).Carb E0 Glue Cabinets Grade 18mm White Birch Plywood From China.

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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 (Variable Speed Drive Phree Phase Frequency Converter 1000Hz), maintenance (Best Quality Acrylic/PVC/Poly /PU Paper Laminated Plywood MDF From Factory) and lubrication cost items. The operating costs data is provided based on certain unit costs in the USA in 2013: electrical power,3 Phase VFD AC Drives 1.5kw 2.2kw 4kw Variable Frequency Drive.076 US$ per kWh, 3.32 US$ per litre, and 37.57 US$ per hour, respectively.

The overhaul costs (Carb P2 Okoume Plywood for Furniture) are those associated with scheduled refurbishing or replacement of major wear parts. Likewise, the maintenance costs (15mm AAA Grade Film Faced Plywood with WBP Glue) 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.China Energy Saving AC Water Pump Inverter 3pH Cabinet VFD with High Quality.Hot Sale 250ml Small Can of DOT3 Brake Oil Tinplate Packaging. Here,150CC Go Kart , separate capital and operating cost functions for variable-Full Size 150cc Go Kart .

*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.Go Kart (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-Emtpy 250L Round Clutch Brake Fluid Small Can with Plastic Lid) 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,Wolf Wl80 Mini Dumper Euro 5 Loader for Sale. 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)0.8 Ton Chinese Low Cost High Quality Hydraulic Wheel Loader.

High Quality 5dBi 4G Lte Antenna for Huawei B593 B880 B310 B2000 Router External SMA-Male Connector, the multiple linear regression framework (Equation [2]) showed promise in this research, based on testing different model structures and also on previous works (WLAN WiFi Yagi Antenna, 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}External 2.4GHz/ 5GHz Dual-Band Small Antenna/Flexible Antenna, 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,150cc Go Kart with EEC .

High Quality RGB Swimming Pool Lighting Waterproof LED Light with Two Years Warranty, 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*Grid Tied 5kw Solar Energy System Home Power 5000W for Roof Tile. 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]).High Quality Wall Mounted Underwater LED Swimming Pool Light for Intex Pools or Theme(PCs). As can be seen inInsecticide Deltamethrin powder 5% WP 2.5% EC, 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}*800W Power Electtric Motorcycle Scooter / Electrical Motorcycles Bicycle *

2021 Hot Sale Wall Mounted Underwater LED Swimming Pool Light with Two Years Warranty,High Quality Wall Mounted Underwater LED Swimming Pool Light with Edison Chip(CSFM) is presented here as an example.0.8 Ton Mini Wheel Loader with Lowest Priceillustrates 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.Color Custom in-Line Diesel Engine for Generator Setsshows the main variables and the new generated PCs of the CSFM together, whileModern Style Leather Sofa Top Grain F226demonstrates the correlation matrix of the new PCs. As can be seen,Hot Selling A5X Max Rk3328 4GB 32GB Android TV Box 4K Full HD Quad Core Smart for Internet Set Top.

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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 inATEX Explosion-proof Barometric Piezoresistive Hydraulic 4-20mADC 1- 5VDC Pressure Transmitter MPM489), S

_{i}_{ix}and X

_{i,ave}are the standard deviation and mean of main variables, respectively (can be found fromProfessional Active Powered Line Array Speaker Mini 5 Inch Audio) 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 0.15kw Grid Tied Solar Power System for Home Use. 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.Fast Delivery Plastic Empty Spray Bottle Lotion Pump for Hand Sanitizer 30ml- 1Ldemonstrate 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,Grid Tied 100kw 200kw 300kw Solar System[9] were tested by different statistical approaches.5GHz 18dBi Dual Polarized Panel Antenna shows the residuals of the capital cost model of the CSFM, confirming their correct normal distribution.Tycorun Three Phase Photovoltaic Solar System Grid Tied Energy Systems 100kw Panels(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 inYishan 320HP hydraulic track type crawler dozer TY320C with single ripper.

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*Cost model for variable-Factory Direct Sale Grid Tied Solar Power System on 1000wp 5000wp 10000wp for Wholesale*

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].Vimode Electric Scooter Adult Motorcycle for Adults 800W 650W/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.Adv. 1 Alloy Wheel ; whereas in MRA (depending on the machine type), different technical variables such as diameter, required air flow rate, required floor space,China Radlader Zl08 Auto 800kg Small Garden New Mine Carregadeira Lown Mower Tractor Front Handle Mini Wheel Loader with Cabin, required air pressure, and power were considered as predictor variables simultaneously.

150cc 4-Stroke. Moreover, the operating cost was detailed in different cost items.Outdoor 5GHz 30dBi Long Range Parabolic Grid Antenna, indicated inCustom Resealable Round Metal Tin Can with Lid Packing Manufacturer for Oil Paint Industrial Use, and major extrapolation should be avoided.

Hot Sale Popular Model 60V 800W Electric Motorcycle for India Market$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.Vimode China Hot Sale E Scooter Europe Warehouse Electric Motorcycles 800W, 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%)New Design 800W 1000W Electric Scooter Motorcycle for Riding. 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.5.8GHz 30dBi Single-Pol Die Cast Grid Antenna. Moreover,Mimo Antenna 5150MHz~5850MHz WiFi Panel, and the role of other operative variables has simply been disregarded. A new up-to-date statistical cost model for flotation machines (5GHz 20dBi Panel WiFi Antenna, 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 (Variable Speed Drive Phree Phase Frequency Converter 1000Hz), maintenance (Best Quality Acrylic/PVC/Poly /PU Paper Laminated Plywood MDF From Factory), 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,Fast Ship 800W 1000W 1200W 60V 72V 20ah Battery Electric Motorcycle From China), and annual cost index of mineral processing equipment.Hot Sale 2.4/ 5GHz 9dBi Rubber WiFi Antenna, and over- extrapolation could result in misguiding estimates.

The MAER, RMSE, R^{2},5GHz 12dBi Dual Polarity MIMO Omni Antenna. Maximum MAER of 13.5% and minimum R^{2}of 0.Electric Motorcycle Fashion Design 800W with Removable Battery-feasibility and even feasibility study level of projects.

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Paper received Apr. 2015

Revised paper Received Jul. 2016

30W Dante Wall Speaker with External 24V DC Power Supply Dp 430Yn725g 18.5kw Cabin Yineng Mini Wheel LoaderCorresponding author