Nordberg ball mill model - Revision history

Alex Doll: /* Calculation description */

2015-05-14T17:14:17Z

Calculation description

Alex Doll at 16:18, 22 April 2015

2015-04-22T16:18:27Z

Alex Doll: /* Calculation description */

2015-04-20T19:16:56Z

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Alex Doll: /* Calculation description */

2015-04-20T19:09:54Z

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Alex Doll: Alex Doll moved page Nordberg model to Nordberg ball mill model: distinguishes what kind of model this is.

2014-05-01T16:35:10Z

Alex Doll moved page Nordberg model to Nordberg ball mill model: distinguishes what kind of model this is.

Alex Doll: /* Calculation description */

2014-02-07T05:14:36Z

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Alex Doll: /* Calculation description */

2014-02-07T05:13:19Z

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Alex Doll at 05:12, 7 February 2014

2014-02-07T05:12:11Z

Alex Doll: Created page with "This model was published by the Nordberg equipment company with versions of it appearing in their "Red Book" equipment sizing manual in the 1970's. The latest version of this..."

2014-01-26T18:36:39Z

Created page with "This model was published by the Nordberg equipment company with versions of it appearing in their "Red Book" equipment sizing manual in the 1970's. The latest version of this..."

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This model was published by the Nordberg equipment company with versions of it appearing in their "Red Book" equipment sizing manual in the 1970's. The latest version of this model published was by the Outokumpu company (now Outotec) publication "The Science of Comminution" (undated, but probably about 2002).

===Inputs===
The model requires three inputs in its original form, and a "density corrected" variation includes a fourth input.
* mill effective inside diameter (to calculate Factor A)
* mill fraction filling of the charge (to calculate Factor B)
* mill fraction of critical speed (to calculate Factor C).
* (for density correction) effective density of the mill charge

===Output===
The model output is the "US horsepower per foot of mill length" where the power is measured at the mill shell. Multiplying this output by the mill effective grinding length and converting the result to modern units of power results in the mill power draw at the shell in kilowatts.

===Calculation description===
Each of the three original inputs are fit to equations based on the Nordberg published tables that generate, respectively, values for Factor A, Factor B and Factor C which are multiplied together.

<math>Factor A = 10^{2.499 \times Log10(inside diam, mm) - 6.957}</math>

<math>Factor B = min(5.2 , 5.2-10^{1.951 \times Log10(50-MillLoad) - 2.66}</math>

<math>Factor C = 10^{0.009 \times speed - 1.412}</math>

The Outokumpu reference gives the base mill charge density for these formulae as 310 lb/ft<sup>3</sup>. This translates to a charge density of 5050 kg/m<sup>3</sup>. Knowing the actual density of the charge allows the correction to be calculated as:

<math>\text{Density correction} = \frac{\text{actual density} kg/m^3}{5050 kg/m^3}

@@ Line 16: / Line 16: @@
 ===Calculation description===
-Each of the three original inputs are fit to equations based on the Nordberg published tables that generate, respectively, values for Factor A, Factor B and Factor C which are multiplied together.  There are slightly different versions of the Factor B for different styles of mills.  The equation presented below is for wet overflow ball mills.
+Each of the three original inputs are fit to equations based on the Nordberg published tables that generate, respectively, values for Factor A, Factor B and Factor C which are multiplied together.  There are slightly different versions of the Factor B for different styles of mills.  The equation presented below is for <u>wet overflow ball mills</u>.
 <math>Factor A = 10^{2.499 \times Log10(inside diam, mm) - 6.957}</math>

@@ Line 1: / Line 1: @@
 [[category:Models]]
 [[category:Mill power draw models]]
-This ball mill power draw model is based on a torque model and empirical measurements made by the Nordberg Equipment Company for use by its sales representatives to size grinding mills.  Slight differences in the equations used allow rod mills, dry ball mills and wet overflow and grate ball mills to be sized.
+This ball mill and rod mill power draw model is based on a torque model and empirical measurements made by the Nordberg Equipment Company for use by its sales representatives to size grinding mills.  Slight differences in the equations used allow rod mills, dry ball mills and wet overflow and grate ball mills to be sized.
 ===History===
 This model was published by the Nordberg equipment company with versions of it appearing in their "Red Book" equipment sizing manual in the 1970's.  The latest version of this model published was by the Outokumpu company (now Outotec) publication "The Science of Comminution" (undated, but probably about 2002).
@@ Line 31: / Line 31: @@
 <math> \text{Power at pinion, HP} =  \text{Factor A} \times \text{Factor B} \times \text{Factor C} \times \text{Density correction} \times \text{EGL, ft}</math>

← Older revision		Revision as of 19:16, 20 April 2015
Line 26:		Line 26:
	The Outokumpu reference gives the base mill charge density for these formulae as 310 lb/ft<sup>3</sup>. This translates to a charge density of 5050 kg/m<sup>3</sup>. Knowing the actual density of the charge allows the correction to be calculated as:		The Outokumpu reference gives the base mill charge density for these formulae as 310 lb/ft<sup>3</sup>. This translates to a charge density of 5050 kg/m<sup>3</sup>. Knowing the actual density of the charge allows the correction to be calculated as:

−	<math>\text{Density correction} = \frac{\text{actual density } kg/m^3}{5050 \text{ } kg/m^3}	+	<math>\text{Density correction} = \frac{\text{actual density } kg/m^3}{5050 \text{ } kg/m^3}</math>
		+
		+	The model result is "horsepower per foot of mill effective grinding length", so multiply the result by the mill EGL to get pinion power draw.
		+
		+	<math> \text{Power at pinion, HP} = \text{Factor A} \times \text{Factor B} \times \text{Factor C} \times \text{Density correction} \times \text{EGL, ft}</math>

@@ Line 20: / Line 20: @@
 <math>Factor A = 10^{2.499 \times Log10(inside diam, mm) - 6.957}</math>
-<math>Factor B = min(5.2 , 5.2-10^{1.951 \times Log10(50-MillLoad) - 2.66}</math>
+<math>Factor B = min(5.2 , 5.2-10^{1.951 \times Log10(50-MillLoad) - 2.66})</math>
 <math>Factor C = 10^{0.009 \times speed - 1.412}</math>
@@ Line 26: / Line 26: @@
 The Outokumpu reference gives the base mill charge density for these formulae as 310 lb/ft<sup>3</sup>.  This translates to a charge density of 5050 kg/m<sup>3</sup>.  Knowing the actual density of the charge allows the correction to be calculated as:
-<math>\text{Density correction} = \frac{\text{actual density } kg/m^3}{5050 kg/m^3}
+<math>\text{Density correction} = \frac{\text{actual density } kg/m^3}{5050 \text{ } kg/m^3}

← Older revision		Revision as of 05:14, 7 February 2014
Line 26:		Line 26:
	The Outokumpu reference gives the base mill charge density for these formulae as 310 lb/ft<sup>3</sup>. This translates to a charge density of 5050 kg/m<sup>3</sup>. Knowing the actual density of the charge allows the correction to be calculated as:		The Outokumpu reference gives the base mill charge density for these formulae as 310 lb/ft<sup>3</sup>. This translates to a charge density of 5050 kg/m<sup>3</sup>. Knowing the actual density of the charge allows the correction to be calculated as:

−	<math>\text{Density correction} = \frac{\text{actual density} kg/m^3}{5050 kg/m^3}	+	<math>\text{Density correction} = \frac{\text{actual density } kg/m^3}{5050 kg/m^3}

← Older revision	Revision as of 16:35, 1 May 2014
(No difference)

← Older revision		Revision as of 05:12, 7 February 2014
Line 1:		Line 1:
		+	[[category:Models]]
		+	[[category:Mill power draw models]]
		+	This ball mill power draw model is based on a torque model and empirical measurements made by the Nordberg Equipment Company for use by its sales representatives to size grinding mills. Slight differences in the equations used allow rod mills, dry ball mills and wet overflow and grate ball mills to be sized.
		+	===History===
	This model was published by the Nordberg equipment company with versions of it appearing in their "Red Book" equipment sizing manual in the 1970's. The latest version of this model published was by the Outokumpu company (now Outotec) publication "The Science of Comminution" (undated, but probably about 2002).		This model was published by the Nordberg equipment company with versions of it appearing in their "Red Book" equipment sizing manual in the 1970's. The latest version of this model published was by the Outokumpu company (now Outotec) publication "The Science of Comminution" (undated, but probably about 2002).