Module2 - Rod and Ball Mill Power Draw

The Metcom Engineering and ManagementSystem for Plant Grinding Operations

MODULE #2:

ROD AND BALL MILL POWER DRAW

Metcom Consulting, LLC© 1992 GPD Co. Ltd. / Metcom Consulting LLC (Rev.4, 2005)


© 1990 GPD Co. Ltd. / Metcom Consulting LLC (Rev.4, 2005))

page

Objectives 1Introduction 2

• Energy and power 3• Mill power draw at the pinion 5

Progress Review 1 8

PART I - Mill Power Draw Calculations 14

Rod mill power draw 15Ball mill power draw 21Accuracy of power draw calculations 27

PART II - Increasing the Power Draw of Grinding Mills 29

Mill volumetric loading 30Mill speed 36Other factors 41

Progress Review 2 43

Closing word 50References 51

Appendix A - Power draw calculations using metric units 52

Glossary 56

TABLE OF CONTENTS

i


© 1990 GPD Co. Ltd. / Metcom Consulting LLC (Rev.4, 2005)

ii

LIST OF FIGURES

page

Figure 1. Tumbling charge inside a grinding mill. 5

Figure 2. Tumbling grinding mill with ring gear and pinion. 6

Figure 3. Power draw versus volumetric loadingcurve for a rod mill. 30

OBJECTIVES

This module will introduce you to rod and ball mill power draw *.

At the end of this module, you will be able to:

• Differentiate between "energy consumed" and "power drawn" by grinding mills.

• Calculate the approximate mill power draw of operating rod mills and ball mills given basic design and operating conditions.

• Specify practical means (and limitations) to increase the power draw of operating rod mills and ball mills in the plant.

There is no prerequisite to this module. You will need a scientificcalculator to perform the calculations.

This module contains two Progress Reviews: one following theIntroduction and one at the end of the module. Estimated time forcompletion is two hours including the two Progress Reviews.



ROD AND BALL MILL POWER DRAW 2


INTRODUCTION

In this module, you will learn about the energy consumptioncharacteristics of rod mills and ball mills.

Energy is the primary input of size reduction processes. Theefficiency of the size reduction process is measured on the basis ofenergy consumption as this energy is delivered to the ore through thegrinding mill. Therefore when studying grinding, we are intimatelyconcerned with the energy consumption characteristics of the grind-ing equipment.



ENERGY AND POWER

Throughout this module, we will be using both units of energyconsumption normally used for motors. The units of energy are the:

• Kilowatt-hour, kwh (metric).• Horsepower-hour, HPh (British).

The units of power are the:

• Kilowatt, kw (metric).• Horsepower, HP (British).

You will need the following conversion factors to convert units frommetric to British and vice-versa:

1 kwh = 1.341 HPh

1 kw = 1.341 HP



Note

Some important definitions follow:

Energy: Energy equals work. Energy is power consumed overtime as the work is done. In terms of units, we have:

Energy consumed = Power (kw) x Time (h) (kwh)

Power: Power is the instantaneous measure of energy drawn per unit of time. In terms of units, we have:

Power drawn = Energy (kwh) / Time (h) (kw)

To help you differentiate between "energy" and "power", rememberthat energy is consumed while power is drawn.

Energy is utilized inside the grinding mill by lifting the charge * on therising side of the rotating shell liners. This is shown in Figure 1.

Figure 1. Tumbling charge inside a grinding mill.

As the mill rotates, the energy is expended by the impact and attritionof the falling and tumbling charge. You can envision the constantwork load created by the charge in suspension against gravity. Thiswork load is proportional to the mass of the charge and the horizontaldistance d between the centre of mass of the charge, (representedby M) and the longitudinal axis of the mill. When the mill is stopped,M falls directly under the longitudinal axis of the mill: D is zero andthe work load is zero.

MILL POWER DRAW AT THE PINION





The power required to lift the charge inside the mill is transmittedthrough the ring gear and pinion. Figure 2 illustrates this event.

Figure 2. Tumbling grinding mill with ring gear and pinion.

There are certain losses in power transmission between the pinionand the charge. For example, losses occur in the mill bearings,where the ring gear and pinion meet, and on the outside of therotating shell due to air resistance. These small losses total less than2 to 3% of the load created by the charge. Furthermore, these lossesare virtually constant (as a fraction of the total load) for all commercialsize tumbling mills.

Throughout the Metcom System, by convention, we refer to the millpower draw at the pinion (unless otherwise noted).

Notes

1. Mill power draw calculations will give you approximate values of mill power draw because they include basic design and operating variables for grinding mills. The basic variables are: mill dimensions, speed and volumetric load *, and charge density.

2. There is a difference between the power at the pinion and the power you read on the kilowatt-meters in the plant. This will be discussed in greater detail in the module on "Power and Charge Level Measurements".

To make sure you understand the information presented in theintroduction to this module, answer the questions in the followingProgress Review.



1 PROGRESS REVIEWEstimated time for completion: 3 minutes

There are six questions in this Progress Review. Refer back to thetext if necessary.

1. Answer the following "true" or "false" questions about why, in the technical sense, we are concerned about the energy consumption characteristics of grinding mills. Check the appropriate box.

True False

a) Energy is the primary input for size reduction to take place.

b) Energy consumption is the basis for measuring grinding efficiency.

c) It is the grinding mill that delivers the energy to the ore.

2. Select the two units of measure normally used for mill energyconsumption.

Btujouleskilowatt-hoursgram-calorieshorsepower-hours





3. Check the appropriate box for the following expressions:

Correct Incorrect

Power consumed

Energy drawn

Power drawn

Energy consumed

4. Give the usual units of measure for grinding equipment which apply to:

Energy, metric system ___________________ British system ___________________

Power, metric system ___________________ British system ___________________

5. A motor has an output rating of 1000 kw. What is the output rating of this motor in British units (HPh)?

Write your answer: ___________________

1 PROGRESS REVIEW(continued)




6. Select the reference point which is used by convention in the industry for "mill power draw":

At the kilowatt meterAt the motor inputAt the motor outputAt the pinionAt the mill shellAt the charge

The answers to these questions follow.




Answers

1. True False

a) Energy is the primary input for size reduction to take place.

b) Energy consumption is the basis for measuring grinding efficiency.

c) It is the grinding mill that delivers the energy to the ore.

2. Btujouleskilowatt hoursgram calorieshorsepower hours

3. Correct Incorrect

Power consumed

Energy drawn

Power drawn

Energy consumed

X

X

X

x

X

X

X

X

x




4. Energy, metric system: kwh British system: HPh

Power, metric system: kw British system: HP

5. 1341 HP = 1000 kw x 1.341 HP / kw

6. At the kilowatt meterAt the motor inputAt the motor outputAt the pinionAt the mill shellAt the charge

Answers (continued)

x



How did you do in this Progress Review?

• If you scored 100%, congratulations!

• If you had problems answering some questions, make sure to go back to the text and understand it clearly before moving on.

This concludes the introduction to the module. In Part I, you will learnhow to calculate power draw at the pinion for rod mills and ball mills.



PART I - MILL POWER DRAW CALCULATIONS

Part I presents the mill power draw equations developed and used byFred Bond and his co-workers.

There have been numerous individuals and organizationsresearching mill power draw characteristics over the years. While allhave arrived at slightly different conclusions, the results are similarwhen the same basic design and operating conditions areconsidered. Some secondary factors such as liner design, feed rateand size are a cause for variations in results and will be discussedlater in this module.

The discussion in this module is limited to rod mills and ball millsoperated under normal, stable operating conditions with the feed ON.Mill power draw may be affected by circuit instability.

The following method for calculating rod mill power draw applies towet grinding overflow rod mills* . The equations presented wereoriginally developed with both the metric and British units. If youprefer to work with metric units when dealing with results from yourplant, use the equations presented in Appendix A.

To estimate rod mill power draw, follow these five steps. Notes onthe presented variables follow.

1. Estimate the weight of the rods, Tr, inside the mill in short tons:

Tr = Vp D2 L 375(short tons) 4 2000

where Vp = Mill volumetric loading, when stationary (fraction)

D = Mill inside diameter (feet) L = Mill inside length (feet)

375 = Average bulk density of a rod charge (lbs/ft3) 2000 = Conversion factor to short tons.

Notes on these items follow.

When all the constants are combined, the equation simplifies to:

Tr = Vp D2 L(short tons) 6.8

Procedure

ROD MILL POWER DRAW

( ) ( )



2. Calculate the mill critical speed *, Cs:

Cs = 76.63 (rpm) šD

3. Calculate the speed of the mill as a % of critical speed, %Cs, using the actual mill speed in revolutions per minute (rpm):

%Cs = Actual mill speed (rpm) Cs (rpm)

4. Calculate the power draw per short ton of rods in the mill, kwr:

kwr = 1.07 D0.34 (6.3 - 5.4 Vp) %Cs kw/short ton of rods

When using this equation, "%Cs" must be entered as a fraction.

5. Calculate the power draw of the rod mill (at the pinion), Prm:

Prm = Tr x kwr(kw)

Procedure (continued)

( )



Notes

1. For the purpose of this module, you can simply assume a value for Vp. In the module entitled "Power and Charge Level Measurements", you will learn how to determine Vp for your mills.

2. For the purpose of this module, the internal diameter of the mill, D, does not need to be exact. Subtract 0.5 foot from the nominal mill diameter (measured inside the shell) to account for the thickness of the liners.

3. You can obtain the actual mill speed by either timing it or by calculating it from the motor speed and gear reduction ratios to the mill shell.

4. The density of a rod charge may vary slightly from 375 lbs per cubic foot for either a brand new rod charge (with no broken pieces of rods in it) or very large rod mills that contain an excessive amount of pieces of rods. Go to the reference by Rowland if either one of these factors applies to your case.

Here is an example on how to estimate Prm.



A wet grinding overflow rod mill has the following characteristics:

Mill dimensions: D = 10 ft (inside diameter)L = 16 ft (inside length)

Mill speed: 18.4 rpmMill volumetric loading: 40% of total mill volume.

To calculate Prm for this mill, we must estimate Tr, Cs, %Cs,and kw :

Tr = Vp D2 L = 0.40 x 102 x 16 = 94.1 short tons 6.8 6.8

Cs = 76.63 = 76.63 = 24.2 rpm šD š10

%Cs = Actual mill speed = 18.4 rpm = 76% Cs 24.2 rpm

kwr = 1.07 D0.34 (6.3 - 5.4 Vp) %Cs

= 7.37 kw/short ton of rods

Prm = Tr x kwr = 94.1 short tons x 7.37 kw/s.t.

= 694 kw

This rod mill will draw approximately 694 kw (931 HP) at the pinionunder the given conditions.

Solve the following exercise.

r

Example

= 1.07 100.34 [6.3 - 5.4 (0.40)] 0.76





Exercise

Given the following characteristics of a wet grinding overflow rod mill,estimate the power draw at the pinion during normal operation.

Mill dimensions: D = 8.5 ft (inside diameter)L = 12 ft (inside length)

Mill speed: 19.1 rpmMill volumetric loading: 42% of total mill volume

What is the power draw at the pinion for this rod mill in both themetric and British units? _____________________________

The answers follow.

Answers

This rod mill draws approximately 347 kw or 465 HP at the pinionunder the given conditions.

Tr = Vp D2 L = 0.42 x 8.52 x 12 = 53.6 short tons 6.8 6.8

Cs = 76.63 = 76.63 = 26.3 rpm šD š8.5

%Cs = Actual mill speed = 19.1 rpm = 72.6% Cs 26.3 rpm

kw = 1.07 D0.34 (6.3 - 5.4 Vp) %Cs



= 347 kw

= 465 HP

Now you know how to calculate the power draw of a rod mill at thepinion. Next, let's see how to calculate the power draw of a ball mill.

= 1.07 8.50.34 [6.3 - 5.4 (0.42)] 0.726



( ) ( )

The following power draw calculations apply to wet overflow ball mills* .The approach to calculate ball mill power draw is the same as for rodmills. However, there is an additional step for ball mills with insidediameters greater than 3 meters (10 feet). In such mills, media sizenoticeably affects power draw and must be considered in thecalculations.

To calculate ball mill power draw at the pinion, follow these six steps.Notes on the presented variables follow.

1. Estimate the weight of the balls inside the mill in short tons, Tb:

Tb = Vp D2 L 290 4 2000

where Vp = Mill volumetric loading, when stationary (fraction)

D = Mill inside diameter (feet) L = Mill inside length (feet)

290 = Average bulk volume of a ball charge (lbs/ft3) 2000 = Conversion factor to short tons.

Notes on these items follow.

When all the constants are combined, the equation simplifies to:

Tb = Vp D2 L (short tons) 8.8

BALL MILL POWER DRAW

Procedure



2. Calculate the mill critical speed, Cs:

Cs = 76.63 (rpm) šD

3. Calculate the mill speed as a % of critical speed, %Cs, using the actual mill speed in revolutions per minute (rpm):

%Cs = Actual mill speed (rpm) Cs (rpm)

4. If D is smaller than 3 meters (10 feet) for your mill, the media size correction factor, S, is zero. Go to step (5).

For ball mills greater than 3 meters (10 feet) in diameter, calculate the media size correction factor, S:

S = B - 0.15 D 2

where B = Make-up ball size (inches)D = Mill inside diameter (feet)

5. Calculate the power draw per short ton of balls in the mill, kwb:

kwb = 3.1 D0.30 (3.2 - 3.0 Vp) %Cs 1 - 0.1 + S

2(9 - 10 x %Cs)

(kw/short) ( ton of ) ( balls )

[ ]






Notes

6. Calculate the power draw of the ball mill (at the pinion), Pbm:

Pbm = Tb x kwb(kw)

1. These calculations are for overflow ball mills. However, full grate discharge mills* draw approximately 15% more power on average than overflow mills with the same internal length.

For dry grinding, grate overflow ball mills, the power draw isapproximately 8 % higher.

2. For the purpose of this module, you need only a rough estimate ofVp. In the module entitled "Power and Charge Level

Measurements", you will learn how to determine Vp for your mills.

3. For the purpose of this module, the internal diameter of the mill, D, needs not be exact. Subtract 0.5 foot from the nominal mill diameter (measured inside the shell) to account for the thickness of the liners.

4. You can obtain the actual mill speed by either timing it or by calculating it from the motor speed and gear reduction ratios to the mill shell.

5. The density of a ball charge may vary slightly from 290 lbs per cubic foot for a brand new ball charge (with very few small balls in it).


[ ]

Here is an example on how to estimate Pbm.

An overflow ball mill presents the following characteristics.


Mill speed: 16.3 rpmMill volumetric loading: 34% of total mill volumeMake-up ball size: 1.5 inches

To calculate Pbm for this mill, we must estimate Tb, Cs, %Cs,and kwb:

Tb = Vp D2 L = 0.34 x 132 x 20 = 130.6 short tons 8.8 8.8

Cs = 76.63 = 76.63 = 21.3 rpm šD š13


Since the mill diameter is greater than 3 meters (10 feet), S must becalculated:

S = B - 0.15 D = 1.5 - (0.15 x 13) = -0.225 2 2

kwb = 3.1 D0.30 (3.2 - 3.0 Vp) %Cs 1 - 0.1 + S

2(9 - 10 %Cs)

= 3.1 x 130.30 (3.2 - 3.0 x 0.34) 0.765 x1 - 0.1 + (-0.225) 2(9 - 10 x 0.765)

Example

[ ]



Exercise

kwb = 10.50 kw per short ton of balls

Pbm = Tb x kwb = 130.6 short tons x 10.50 kw/short tonof balls of balls

= 1371 kw

This ball mill draws approximately 1371 kw (1839 HP) at the pinionunder the given conditions.

Solve this exercise.

Given the following characteristics of an overflow ball mill, estimatethe power draw at the pinion during operation in both metric andBritish units.


Mill speed: 14.1 rpmMill volumetric loading: 35% of total mill volumeMake-up ball size: 3 inches

Write your estimate of the power draw in both units:

The answers follow.



The ball mill draws approximately 2618 kw, or 3511 HP, at the pinionunder the given conditions.

Tb = Vp D2 L = 0.35 x 162 x 23 = 234.2 short tons 8.8 8.8

Cs = 76.63 = 76.63 = 19.2 rpm š D š 16


Since the mill diameter is greater than 3 meters (10 feet), S must becalculated:

S = B - 0.15 D = 3.0 - (0.15 x 16) = +0.300 2 2

kw = 3.1 D0.30 (3.2 - 3.0 Vp) %Cs 1 - 0.1 + S

2(9 - 10 %Cs)

= 3.1 x 160.30 (3.2 - 3.0 x 0.35) 0.734 x

1 - 0.1 + (0.300) 2(9 - 10 x 0.734)

kwb = 11.18 kw per short ton of balls.

Pbm = Tb x kw = 234.2 short tons x 11.18 kw/short ton of balls of balls

= 2618 kw

= 3511 HP

Next, let's look at the accuracy of these power draw calculations.

Answers



[ ]

[ ]

ACCURACY OF POWER DRAW CALCULATIONS

The method presented in this module excludes a number ofsecondary factors relative to power draw. Some of these factors are:

1. The shape of the mill ends (flat, partially conical, or conical).

2. Density variation of steel versus cast media.

3. Charge density variation due to media shape (slugs versus balls and degree of distortion of worn media).

4. The density of the solids and slurry in the mill.

5. The size and rate of feed to the mill. These affect volumetric loading by causing the charge to shrink or swell.

6. Liner design and degree of wear.

7. Details of the discharge design (size of trunnion opening or grate locations).

8. The presence of a scoop or other energy consuming type of feeder.

These secondary factors may vary in importance from one plant toanother. They are included in certain methods for power drawcalculations; however, as previously mentioned, most methods giveresults similar to the method presented in this module.

You may be surprised to note the effect of certain factors on millpower draw. Here are some examples:

• Increasing the feed rate to a rod or ball mill decreases the power draw slightly due to the effect of charge swelling (M gets closer to the longitudinal axis of the mill and d gets smaller).

• As liners wear, lifting action is lost. However, resulting power losses may be more than offset by increased internal mill dimensions with liner wear.



Your approximations of mill power draw will generally beconservative, i.e., mills will draw at least as much power ascalculated.

The calculated values of Prm and Pbm, determined fromthe method presented in this module, are accurate to+ 10 to 15% of the "true" power draw of a mill.

You can compare a calculated power draw value to the power drawderived from plant instrument readings (see the module entitled"Power and Charge Level Measurements". With properly calibratedplant instruments and good charge level measurements (also see themodule just listed), the two power draw values will agree within 10 to15%.

In this section, you have learned how to calculate approximate valuesof power draw for rod mills and ball mills. You have also learnedabout secondary factors which affect power draw.

In the second and last part of this module, you will learn how toincrease the power draw of mills in your plant.





Your approximations of mill power draw are not very accurate in anabsolute sense. However, they are quite accurate in a relativesense for the mills in your plant.

To change the power draw of a mill in the plant (the objective isalmost always an increase), we can use the equations presented inthis module to see how changes in the mill design and operatingconditions will affect mill power draw.

If the motor has (or is enlarged to) sufficient capability, you canincrease the power draw to either:

• Increase grinding capacity (in terms of tonnage and/or fineness).

• Effectively treat a tougher ore.

The following discussion covers possible ways of increasing thepower draw of rod and ball mills in the plant and practical andeconomic limitations.

PART II - INCREASING THE POWER DRAW OF GRINDING MILLS



Increasing the mill volumetric load (when possible) is the simplestway of increasing mill power draw. Figure 3 shows a typical curvedepicting the relationship between power draw at the pinion and millvolumetric loading for a rod mill.

Figure 3. Power draw versus volumetric loading curve for a rod mill.

This curve is basically the same for ball mills except that it may peakat a slightly lower charge level.

It is recommended to operate rod mills and ball mills at a volumetricloading no greater than 40 to 45%. Because the curve levels off (asshown in Figure 3), a higher loading contributes little to an increase inpower draw, but will naturally result in greater media consumption.

Some very large overflow ball mills cannot sustain a volumetricloading much greater than about 35%. At higher levels, balls may bedischarged with the slurry or may occasionally (and dangerously) flyout of the mill during operation. When the mill is stopped, they mayalso roll out of the discharge opening.

MILL VOLUMETRIC LOADING

If your mill operates at a low charge level, you may wish to increasethe charge level to increase the power draw. You can estimate thepotential increase in power draw from both:

• A set of power draw versus volumetric loading measurements.

• The relationship between volumetric loading and power draw as characterized by the equations already presented.

For rod mills and ball mills, follow this procedure to estimate apotential increase in power draw from an increase in volumetricloading.

1. For rod mills, enter the known set of values of Prm and Vp to estimate the constant in the following equation:

Prm = constant x Vp (6.3 - 5.4 Vp)

This equation is a combination of the equations in steps (1) and (4) of the rod mill power draw calculations procedure.

2. For ball mills, enter the known values of Pbm and Vp to estimate the constant in the following equation:

Pbm = constant x Vp (3.2 - 3.0 Vp)

This equation is a combination of the equations in steps (1) and (5) of the ball mill power draw calculations procedure.

3. Substitute the desired value of Vp in the calibrated equation for your mill. The resulting value of power draw, Prm or Pbm, gives the anticipated increase (or decrease) in power draw.

Procedure



Here is an example.

The average power draw of a rod mill was measured to be 310 kw atthe pinion, corresponding to an average volumetric load of 35%. Thepotential for increasing the power draw for a mill volumetric loading of40% can be calculated using this equation:

Prm = constant x Vp (6.3 - 5.4 Vp)

Substituting the known values of Prm and Vp, the constant isestimated to be 201:

310 = constant x 0.35 (6.3 - 5.4 x 0.35)

The equation for this mill (assuming other conditions such as linerdesign and condition, feed, etc., are held constant) is therefore:

Prm = 201 x Vp (6.3 - 5.4 Vp)

For a new desired value of Vp of 40%, the expected power draw is:

Prm = 201 x 0.40 (6.3 - 5.4 x 0.40)

Prm = 333 kw

If you increase the volumetric load of this rod mill from 35 to 40%, theaverage power draw will increase from 310 to 333 kw. Thisrepresents an increase of approximately 7%.


Example





Exercise

The average power draw of a ball mill was measured to be 550 kwat the pinion, corresponding to a volumetric loading of 38%.

Questions

1. What is the potential for increasing the power draw of the ball mill if the volumetric load is increased to 45%?

2. What will be the likely effect on ball consumption over the long term?

Write your answer: _______________________________

The answers follow.

Answers

1. The power draw could be increased to 585 kw from 550 kw.

The constant in the power draw equation for ball mills equals 703:

Pbm = constant x Vp (3.2 - 3.0 Vp)

550 = constant x 0.38 (3.2 - 3.0 x 0.38)

If you substitute 45% in the calibrated equation, Pbm equals 585 kw:

Pbm = 703 x 0.45 (3.2 - 3.0 x 0.45)

2. Media consumption will increase.



Notes

1. Increasing the media charge level of a mill up to 50% of the mill volume is normally within the mechanical design limitations of the equipment. However, sometimes this does not hold true, especially for very large ball mills that were designed for relatively low charge levels. Always check with the equipment manufacturer before increasing charge levels by any significant amount.

2. Check the motor rating against the present motor power output measurements to make sure it will not become overloaded at the higher power draw.

3. When you add balls to the ball mill, the increase in power draw should be noticeable. As you approach the peak of the power draw versus volumetric loading curve, power draw will no longer increase. You will learn how to determine the particular relationships between power draw and volumetric loading in the module entitled "Power Draw and Charge Level Measurements".



Power draw is directly proportional to mill speed over the normaloperating range of a rod mill. The following equation (previouslyshown on page 16) illustrates this:

kwr = 1.07 D0.34 (6.3 - 5.4 Vp) %Cs kw/short ton of rods

This is also virtually true (to a reasonable level of accuracy) for ballmills: the second term containing %Cs in the following equation(previously shown on page 22) has a negligible effect on power draw:

kw = 3.1 D0.30 (3.2 - 3.0 Vp) %Cs 1 - 0.1 + S

2 (9 -10 %Cs)

Consider 80% of critical speed as the normal practical limit for bothrod and ball mills (consult with Metcom if you are considering a higher%Cs).

Mill speed can be expressed in terms of either rpm or % of millcritical speed for purposes of power draw calculations. They aredirectly proportional to each other.

The normal method of increasing mill speed is by changing the pinionto one with a larger number of teeth. The speed increase (andtherefore the power draw increase) is directly proportional to the ratioof the number of teeth in the new and old pinions:

Speed increase = # teeth in the new pinion (ratio) # teeth in the old pinion

MILL SPEED

[ ]

( )

kw/short ton of balls

( )





If you change a pinion that has 19 teeth to one that has 21 teeth on arod mill, the speed increase will be 10.5%:

21 teeth = 1.105 (10.5%) 19 teeth

If the rod mill normally draws 500 kw, the new power draw will be:

500 kw x 21 teeth = 553 kw19 teeth

This estimate holds assuming that no mechanical or electricalrestrictions apply, and the mill is operated at the same charge level.

Using the ratio of the number of teeth on pinions is the simplest wayto estimate an expected increase in mill power draw. Alternatively, ifthis change in pinion increases the mill speed from 20 rpm to 22 rpm,the new power draw can also be estimated from the old power draw(500 kw):

500 kw x 22 rpm = 550 kw 20 rpm

The new % of critical speed can be estimated by multiplying the old%Cs (70%) by the ratio of the teeth or rpm created by the change:

70% x 21 teeth = 70% x 22 rpm = 77% 19 teeth 20 rpm


Example



Exercise

The average power draw of a rod mill was measured to be 310 kw atthe pinion. The mill operates at 17.0 rpm (equivalent to 67% ofcritical speed).

Questions

1. What is the potential for increasing the mill power draw if you increase the mill speed to 19.3 rpm by a pinion change?

2. Is this new % of critical speed reasonable for this mill?

Write your answer:

The answers follow.



Answers

1. The new power draw should be 352 kw:

310 kw x 19.3 rpm = 352 kw 17.0 rpm

2. Yes. The new % of critical speed is 76%. This is less than the maximum recommended of 80%.

67% x 19.3 rpm = 76%17.0 rpm

Changing the mill pinion requires that you:

a) Verify the feasibility of design of a new pinion with the desired number of teeth with the mill (or pinion) supplier.

b) Verify the mechanical and electrical design of all other drive components with the mill supplier, particularly for starting the mill.

c) Verify that the mill can be shifted over to accommodate the larger diameter of the new pinion (if an increase in speed is the goal).

d) Once again, verify that the motor is rated to handle the new power.

Increasing mill speed can have an advantageous effect on mediaconsumption in addition to increasing mill power draw. The savingson media consumption expected by operating at reduced chargelevel and increased speed (to achieve the same net power draw) areoften very favourable.





Aside from adding new mills to a circuit, there are a few other meansof increasing rod or ball mill power draw that are not usually practicalfor this singular purpose. These include the followingpossibilities:

A) Media material: Forged or cast steel has a slightly higher solids density than some cast irons. If you are using cast iron balls, it may be possible to increase power draw slightly (i.e., 0 to 5%) by changing media material. However, media cost and consumption rate will usually be the key factors which determine media material selection.

B) Media size and shape: As indicated by the media size correction factor S, the use of larger balls will cause a particular mill to draw slightly more power. However, the effect is quite small and grinding efficiency will definitely be an overriding concern.

Non-spherical shapes (e.g., slugs) tend to increase packing density of the charge and hence increase power draw for an equal charge level. However, the material consumption rate and grinding efficiency will once again take precedence.

C) Mill dimensions: Increasing the mill diameter or length is rarely feasible. Liner design and liner wear profile throughout its life affect power draw noticeably. (For example, when new liners are installed in a rod mill, power draw is often noted to decrease). The use of higher lifters willl also tend to increase power draw slightly. However, maintenance costs and wear life will

usually be overriding factors in the liner design.

The weight of the liners themselves does not affect power draw as the complete mill shell assembly is a rotating balanced mass. Consequently, rubber versus steel lining (of similar overall

OTHER FACTORS

thickness) does not noticeably affect mill power draw.

D) Grate discharge versus overflow ball mills: A grate discharge ball mill will draw approximately 15% more power than an overflow flow mill of the same internal dimensions. This will offset the loss in mill length if you decide to convert an overflow mill to a grate discharge as a method of trying to improve grinding efficiency.

E) Water usage (at the ball mill feed): The effect is minor but sometimes measureable. The overriding concern is grinding efficiency.

This section wraps up the information presented to you in thismodule. Review the contents of the module in Progress Review 2.



2 PROGRESS REVIEWEstimated time for completion: 5 minutes

This Progress Review contains four problems. Refer back to the textwhen necessary.

1. John has the following information on the rod mill in his plant:


Mill speed: 17.5 rpmMill volumetric loading: 43% of total mill volume

What is the power draw of this rod mill when operated under these conditions? (Reference: page 15)

Write your answer in both metric and British units: ___________ ___________




2. Continuing on Problem #1, John wishes to increase the power draw of the mill by raising the volumetric load to 46%.

What is the expected mill power draw for the new load? (Reference: page 31)

Write your answer in both metric and British units: ____________ ____________






3. John has raised the mill volumetric load to 46%. To further increase mill power draw, he has studied the physical and economical impact of replacing the actual pinion (18 teeth) by a new pinion (20 teeth).

a) What is the expected power draw following this change? (Reference: page 37)

b) What is the expected rpm following the change in pinion? (Reference: page 36)

c) What is the expected % of critical speed following this change? (Reference: page 37)



4. It is necessary to increase the grinding capability of an overflow ball mill by approximately 10% because mining is reaching a zone that contains ore which is tougher to grind.

From the following list, select the two most practical and usefulmethods for increasing the power draw of this ball mill.

Increase the size of the motor

Increase the mill speed

Increase the charge volume

Increase the tonnage feed rate

Increase ball diameter

The answers and solutions to the Progress Review follow.



Answers

1. 639 kw or 857 HP

Tr = Vp D2 L = 0.43 x 102 x 15 = 94.9 short tons 6.8 6.8

Cs = 76.63 = 76.63 = 24.2 rpm šD š10


kwr = 1.07 D0.34 (6.3 - 5.4 Vp) %Cs

= 1.07 100.34 [6.3 - 5.4 (0.43)] 0.723



= 639 kw

= 857 HP

2. 655 kw or 878 HP

The constant in the equation for rod mills equals 373.6:

639 kw = constant x 0.43 x (6.3 - 5.4 x 0.43)

The power draw at the pinion will be:

Prm = 373.6 x 0.46 x (6.3 - 5.4 x 0.46)= 655 kw= 878 HP






3. a) 728 kw = 655 kw x 20 teeth 18 teeth

(Remember that John has raised the volumetric loading. The power draw is now 655 kw, not 639.)

b) 19.4 rpm = 17.5 rpm x 20 teeth 18 teeth

c) 80.3 = 72.3 x 20 teeth 18 teeth

4. Increase the size of the motor

Increase the mill speed

Increase the charge volume

Increase the tonnage feed rate

Increase the size of balls

In order of practical and economical priority, increasing the mill volumetric loading should be considered prior to changing the mill speed.

X

X

Answers (continued)



This concludes Progress Review 2. How did you do?

If you scored 100%, good work! If not, study the solutions carefully.



CLOSING WORD

You have completed the module on rod mill and ball mill power draw:congratulations!

This module is a prerequisite to the module entitled "Power andCharge Level Measurements". In that module, you will learn how toestimate the actual power draw and volumetric load of your grindingmills.



REFERENCES

Bond, F. C., "Crushing and Grinding Calculations", reprintedfrom British Chemical Engineering, Part I - June 1961,Part II - August 1961, with additions and revisions, April 1962.

Rowland, C. A., "Selection of Rod Mills, Ball Mills, Pebble Mills,and Regrind Mills", Design and Installation ofComminution Circuits, SME of AIME, New York, 1982,Chapter 23, pp. 393-438.

1. Estimate the weight of rods, Tr, inside the mill in metric tons:

Tr = Vp D2 L 6.008(metric tons) 4

where Vp = Mill volumetric loading (fraction) D = Mill inside diameter (meters) L = Mill inside length (meters)

6.008 = Average bulk density of a rod charge (tons/m3)

The equation simplifies to :

Tr = Vp D2 L(metric tons) 0.2119


Cs = 42.31 (rpm) šD

APPENDIX A

POWER DRAW CALCULATIONS USING METRIC UNITS

Rod Mill Power Draw Calculations

( )





3. Calculate the speed of the mill as a % of critical speed, Cs:

%Cs = Actual mill speed (rpm)Cs (rpm)

4. Calculate the power draw per metric ton of rods in the mill, kwr :

kwr = 1.766 D0.34 (6.3 - 5.4 Vp) %Cs kw/metric ton of rods

5. Calculate the power draw of the rod mill (at the pinion), Prm:

Prm = Tr x kwr(kw)

( )

1. Estimate the weight of balls, Tb, inside the mill in metric tons:

Tb = Vp D2 L 4.646 4

where Vp = Mill volumetric loading (fraction) D = Mill inside diameter (meters) L = Mill inside length (meters)

4.646 = Average bulk density of a ball charge

The equation simplifies to :

Tb = Vp D2 L(metric tons) 0.2740


Cs = 42.31 (rpm) šD

3. Calculate the mill speed as a % of critical speed, %Cs

%Cs = Actual mill speed (rpm)Cs (rpm)

Ball Mill Power Draw Calculations

( )

(tons/m3 )



4. Calculate the value of S if your mill has a diameter greater than 3 meters (10 feet):

S = 0.3937 B - 0.4921 D 2

where B = Make-up ball diameter (cm)D = Mill inside diameter (m)

5. Calculate the power draw per metric ton of balls in the mill, kwb:

kwb = 4.879 D0.30 (3.2 - 3.0 Vp) %Cs 1 - 0.1 + S

(kw/metric 2(9 - 10 %Cs)

ton of balls)

6. Calculate the power draw of the ball mill (at the pinion), Pbm:

Pbm = Tb x kwb(kw)



[ ]

GLOSSARY

Charge: The charge is composed of grinding media, solids, andwater.

Full grate discharge mills: A grinding mill from which the pulp isdischarged through a grate. "Full" grate implies that thegrate openings extend over the full diameter of the mill.This results in a low pulp level in the mill.

Mill critical speed: The minimum mill rotational speed at which asmall particle will centrifuge on the internal wall of a grind-ing mill.

Mill power draw: The instantaneous work load created by the liftingand tumbling of the charge measured at the pinion.

Overflow discharge rod/ball mills: A grinding mill from which theslurry is discharged through the opening in the trunnionbecause of the pulp level in the mill. This results in a highpulp level in the mill.

Volumetric load: The fraction or percentage of the mill internalvolume that is occupied by the (bulk of the) grinding mediacharge (voids and media).



Documents

Module2 - Rod and Ball Mill Power Draw