md>Scott.Munro |
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Revision as of 13:22, 2 March 2023
Description
This article describes the Nitta method for estimating the power draw of a vertical stirred mill.[1]
Model theory
The Nitta approach computes mill power as:
where:
- is the net power draw of the mill, i.e. excluding mill drive losses (kW)
- is the gross power draw of the mill, i.e. including mill drive losses (kW)
- is the mill drive efficiency (kW/kW)
- is the power constant (kW), suggested.
- is mill height (m)
- is the fraction of mill volume occupied by the media charge, void space and stirrer below the charge level (v/v).
- is the fraction of mill volume occupied by the stirrer below the level of the media charge (v/v).
- is the diameter of the stirrer (m)
- is the gap between the inside wall of the mill and the stirrer (m)
- is the rotational speed of the stirrer (rps)
Adopting a similar approach as the Hogg and Fuerstenau tumbling mill power model, the net power draw, , may be separated into its contributing constituents:
where:
- is the power drawn by the ball component of the mill load (kW)
- is the power drawn by the interstitial slurry component of the mill load (kW)
- is the volumetric fraction of interstitial void space in the charge (usually 0.4) (v/v)
- is the density of balls (t/m3)
The apparent charge density, , may be computed as:
where is the density of slurry (t/m3).
The slurry density, , may be computed as:
where is the mass fraction of solids in the slurry (w/w), and is the densityy of solid ore particles (t/m3).
Additional notes
The Nitta model does not include a term for charge density, which may compromise its ability to predict mill power draw with alternative grinding media materials, ore densities or feed solids fractions.
Excel
The Nitta mill power model may be invoked from the Excel formula bar with the following function call:
=mdMillPower_Nitta(Parameters as Range)
Invoking the function with no arguments will print Help text associated with the model, including a link to this page.
The Parameters array and model results are defined below in matrix notation, along with an example image showing the selection of the same arrays in the Excel interface:
SysCAD
The Nitta power model is an optional calculation for stirred mill units. If selected, the input and display parameters below are shown.
Tag (Long/Short)
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Input / Display
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Description/Calculated Variables/Options
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Nitta
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HelpLink
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Opens a link to this page using the system default web browser. Note: Internet access is required.
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MillDiameter
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Input/Display
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Diameter of the mill (inside liners).
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MillHeight
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Input/Display
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Height of the mill.
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ScrewDiameter
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Input/Display
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Diameter of the screw stirrer.
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ScrewSpeed
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Input/Display
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Rotational speed of the screw stirrer.
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ScrewVolFrac
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Input/Display
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Volume occupied by screw stirrer as a fraction of mill volume.
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BallFilling
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Input/Display
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Volumetric fraction of the mill filled with balls, including slurry and interstitial voids between balls.
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PowerConstant
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Input
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Coefficient of the power equation.
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PowerLosses
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Input
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Fraction of power lost due to mill drive efficiency ().
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SolidsFraction
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Display
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Mass fraction of solids in the slurry phase.
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OreDensity
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Display
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Density of solids.
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BallDensity
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Input/Display
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Density of balls.
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ScrewWallGap
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Display
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Distance between mill wall and screw stirrer.
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ChargeVolume
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Display
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Volume of media charge in the mill.
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BallMass
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Display
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Mass of balls in the mill.
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InterstitialSLMass
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Display
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Mass of slurry occupying charge void space.
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RhoSlurry
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Display
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Density of slurry phase.
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ApparentDensity
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Display
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Density of total charge (including balls, slurry and voids).
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BallsPower
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Display
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Power drawn by the ball component of the mill load.
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SlurryPower
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Display
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Power drawn by the interstitial slurry component of the mill load.
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NetPower
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Display
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Net power drawn by the mill (excluding drive inefficiencies).
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GrossPower
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Display
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Gross power drawn by the mill (including drive inefficiencies).
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See also
References
- ↑ Nitta, S., Furuyama, T., Bissombolo, A. and Mori, S., 2006, September. Estimation of the motor power of the tower mill through dimensional analysis. In Proceedings of 23rd International Mineral Processing Congress (pp. 3-8).