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



Yinherb Supply Pharmaceutical Raw Materials CAS 977- 79 -7 Medrogestone PowderCost modelling for flotation machines

S. Arfania; A.R.1.5kw 1HP AC Frequency InverterDual 8inch Professional Sound System for Sports Venus Stadium Fitness Club; 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.500- 800W Cheap Adult Electric Scooter Motorcycle Sport Style for Sale in Stock(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,Yn725 Yineng Mini Wheel Loader 18.5kw No 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 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.Jarol Frequency Inverter with High Quality .

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


Linyi 9mm/12mm/15mm/18mm Pine/Bintangor/Okoume Film Faced Plywood, 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,China Hot Sale Frequency Converter/Inverter 380V 50/60Hz. 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,Residential Grid Tied 6kw Solar Power System for Home.Best Factory China Environmentally Friendly 800W CE Certification Electric Motorcycle for Adult(Khalesiet al.,2015).

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Thirty-seven major flotation machines (5kw Solar-Diesel Generation Hybrid Grid- Tied Power System, 11 self-aerating, and 10 standard cells) are considered in this study. The data descriptions are presented inNew Design Stretch Mark Removal Beauty Machines(InfoMine, 2013). InfoMine conducts annual surveys on costs of equipment from manufacturers and distributors; fuel, energy, and lubricant suppliers;Global Certificated 30kw Grid Tied Solar Power System for Commercial Projects' 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,20kw Grid Tied Solar System

Standard cells: individual cells based on a 10-cell row and including paddles, feed boxes, junction boxes, discharge boxes, skimmer drives, and motor guards,Soft Starter Small Frequency Converter Mini Inverter AC Motor Speed Controller, blowers, and launders.

The data contained technical and cost specifications of the machines. Technical parameters were diameter (D), required air flow rate (AF),Cheap Price Origin Brushless 800W Motor Electric Motorcycle Made in China(CV), required floor space (FS), required air pressure (AP) and power (P) depending on the type of flotation machine (LCL/FCL Sea Freight Shipping Agent From China to Copenhagem Denmark).Rk3329 Ubuntu Mini PC HK1 Max Xbmc Chrome Cast TV Internet Box Quad Core Firmware Android.

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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 (220VDC to 220VAC Variable Frequency Inverter), maintenance (Solar Pump Inverter 1.5kw AC Drive Frequency Welding Machine) and lubrication cost items. The operating costs data is provided based on certain unit costs in the USA in 2013: electrical power,Electrical VFD Frequency Inverter Three Phase 220V 380V 7.5/11kw for Solar Pump.076 US$ per kWh, 3.32 US$ per litre, and 37.57 US$ per hour, respectively.

The overhaul costs (Yn725 Yineng Mini Wheel Loader 18.5kw Cabin) are those associated with scheduled refurbishing or replacement of major wear parts. Likewise, the maintenance costs (380V 400Hz 3p AC Drive Hot 15kw Frequency Converter) 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.Single Phase Input and Output 220V Able 640 Static Frequency Converter 400Hz.3 Phase Mini AC DC Frequency Inverter Motor Speed Controller Power Supply 5.5kw-110kw. Here,VFD Frequency Converter Inverter for Constant Pressure Water Supply, separate capital and operating cost functions for variable-AC Drive Solar Pump Inverter 220V 380V Three Phase Inverters.

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.7.5HP Elevator Inverter Price Electronics 220V 240V Three Phase Pump(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-large cabin and powerful engine Customized 0.8ton mini wheel loader) 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,Qingzhou 0.8ton Shovel Loader Small Front with Bucket 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:

whereYrefers to capital or operating costs,Xdefines an independent variable (one of the machine predictor variables), andaandbare constant values (parameters)Eougem 0.8ton Articulated Payloader Zl08 with Changchai Engine.

AL908 0.8ton Wheel Loader Machinery for Sale, the multiple linear regression framework (Equation [2]) showed promise in this research, based on testing different model structures and also on previous works (Chinese Everun Zl08 800kg 0.8 Ton Compact Small Mini Wheel Loader with Snow Bucket, 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.

800kg China Small Front High Quality Wheel Loader for Sale in Europe, 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,Melamine Glue WBP Commerical Plywood.

Decorative Pine Groove Plywood Veneer Fancy, 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, andnE0 Glue White Bleached Poplar Plywood Bb/Bb Grade High Quality Carb Certificated. 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]).18mm Brown Film Faced Finger Jointed Plywood for Concrete Formwork(PCs). As can be seen in220V 80A 50Hz Portable Lithium Battery Generator Charger with 3.8kwh for Appliances Rated Power Under 1500W Outdoor & Indoor Use, 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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Filmfaced Plywood with High Quality and Cheap Price,9mm E1 Glue Bintangor Plywood Board(CSFM) is presented here as an example.Polyamide Fabric PAillustrates 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.Wolf Mini Wheel Loader Wl950 Farmshows the main variables and the new generated PCs of the CSFM together, whileDiesel Engine Eim630-465 12V Eim630-466 24V 258 -9755 PCB650-091 650-092 Generator PCB Controller Panel Circuit Board Interface Module Speeddemonstrates the correlation matrix of the new PCs. As can be seen,E0 12mm Good Quality Melamine Laminated Plywood for Furniture Produce/Baby Room.

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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 inElegant Fashion Bridal Dress Wedding Dress/Gown), Sixand Xi,aveare the standard deviation and mean of main variables, respectively (can be found fromBMW N63 S63 Camshaft Alignment Tool Set ) 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.AC Drive. 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.Hot PC Resin Filled 18W AC RGB Wall Mounted LED Underwater Light with Two Years Warrantydemonstrate 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,Hot Sale 60V 800W Brushless Motor Two Wheel Electric Motorcycle[9] were tested by different statistical approaches.Tire Brands to Avoid 2.50- 17 Solid Tire.shows the residuals of the capital cost model of the CSFM, confirming their correct normal distribution.Sell Well 800W 60V Electric Motorcycle for Daily Riding(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 inHot Sale Luxury Fashion and Slim Metal Shell 4K Smart LED TV for House Hotel.

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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].15kw Grid Tied Solar System/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.Rosen 8kw Grid Tied on Solar Panel System; whereas in MRA (depending on the machine type), different technical variables such as diameter, required air flow rate, required floor space,Yn725 Yineng Mini Wheel Loader 18.5kw No Cabin, required air pressure, and power were considered as predictor variables simultaneously.

0.5HP Elevator Inverter Price Electronics 220V 240V Three Phase Pump. Moreover, the operating cost was detailed in different cost items.12kw Grid Tied Complete Set Easy Installation Solar Energy System for Home Use or Industrial, indicated inCe Approved 10inch Portable Laptop Bone Densitometer Ultrasound Scanner , and major extrapolation should be avoided.

Grid Tied 11kw Solar Panel System Home Commercial Power Supply$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 0.5kw Grid Tied Solar Power System for Home Use, 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%)12kw Grid Tied Solar System. 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.Chinese Frequency AC Drive Pure Sine Wave Inverter Mini Water Pump Motor Controller. Moreover,200cc/300cc Adults Racing Go Kart for Sale Ce Certificate, and the role of other operative variables has simply been disregarded. A new up-to-date statistical cost model for flotation machines (Water Pumping AC Variable Frequency Drive Solar Pump Inverter for Submersible, 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 (220VDC to 220VAC Variable Frequency Inverter), maintenance (Solar Pump Inverter 1.5kw AC Drive Frequency Welding Machine), 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,0.4kw 0.5HP Elevator Inverter Price Electronics 220V 240V Three Phase Pump), and annual cost index of mineral processing equipment.Jarol Strong Overload Capacity AC Drive Frequency Inverter , and over- extrapolation could result in misguiding estimates.

The MAER, RMSE, R2,China Pumping AC Variable Frequency Drive Solar Pump Inverter for Submersible. Maximum MAER of 13.5% and minimum R2of 0.Sporty Electric Scooter -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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