AMIT 135: Lesson 8 Rod Mills


At the end of this lesson students should be able to:

  • Explain the use of rod mills in mineral industry.
  • Explain rod mill operation.
  • Recognize different design parameters of rod mills.
  • Explain problems associated with rod milling.
  • Summarize considerations in rod mill selection

Reading & Lecture



  • Used as the primary comminution unit in a grinding circuit.
  • Rods are placed parallel along the length of the rod mill.
  • Rods are 150mm shorter than the mill length.
  • Breakage occurs more from cascading than cateracting.
  • The product size distribution is narrower than a ball mill but significantly coarser.
  • Most are overflow discharge type.
  • Length-to-diameter= 1.4 to 2.3.
  • Mill length = 7 meters.

Rod Mill-Ball Mill Circuits

Diagrams of mill circuits
Diagrams of mill circuits [image: (135-8-2)]


Rod Mill Operations

  • Designed to accept feed from a secondary crusher.
  • Feed particle size = 6 – 25 mm.
  • Peripheral speed = 85- 146 m/min
    (280 – 480ft/m in)
  • Reduction ratio = 2 – 20 depending on material. Typically R = 8.
  • Rod Mill Charge:
    • Typically 45% of internal volume; 35% – 65% range
    • Bed porosity typically 40%.
    • Height of bed measured in the same way as ball mills.
    • Bulk density of rods = 6.25 tons/m3
  • In wet grinding, the solids concentration 1s typically 60% – 75% by mass.
A rod in situ and a cutaway of a rod mill interior.
A rod in situ and a cutaway of a rod mill interior.
[image: (135-8-3)]



Rod Dimensions

  • Rod tangling is a problem that should be avoided by using straight rods.
  • Rods < 6 meters are generally never straight.
  • Rods should be 152mm shorter than mill length.
  • Rod life is maximized of rod length-to-mill diameter is maintained between 1.4 to 1.6.
  • Rods wear unequally with thin rod formed at the feed end and forming an elliptical shape.
  • Rod diameter is a function of:
    • Ore Work Index
    • Ore Feed Size
    • Ore Density
  • Rod diameter can be estimated by the expression (Rowland & Kjos):d↓R = 25.4[F↓80↑0.75 / 160 (W↓iρ↓S / 100Φ↓C (3.281D) ↑0.5) ↑0.5] mm
Diagram of a charged rod mill interior
Diagram of a charged rod mill interior
[image: (135-8-4)]



Reduction Ratio

  • Reduction ratio ranges from 2 to 200.
  • Typical reduction ratio = 8.
  • The optimum reduction ratio can be determined from the following expression:R↓0R = 8 + 5L/D



Rod Mill Capacity

Mill capacity is dependent on:

  • Mill Characteristics (length, diameter, rotation speed, lifters)
  • Feed Characteristics (work index)
  • Reduction Ratio

Under given load and particle size requirement, capacity is a function of mill length and diameter:

Q = kLD 2+N

N  is related to mill diameter which decreases with larger diameters k a constant equal to π /4.

A chart showing rod mill capacity vs. mill diameter
A chart showing rod mill capacity vs. mill diameter
[image: (135-8-5)]
A chart showing rod mill capacity vs. mill length
A chart showing rod mill capacity vs. mill length
[image: (135-8-6)]
A chart showing rod mill capacity vs. reduction ratio
A chart showing rod mill capacity vs. reduction ratio
[image: (135-8-7)]



Rod Mill Capacity Problems

  • Difficulty in manufacturing perfectly straight rods.
  • Tangling of rods.
  • Swelling of the charge near the feed end.
  • Increasing slurry density due to loss of water.
  • Faulty liners and lifters.
Diagram of tangled rods
Diagram of tangled rods
[image: (135-8-8)]


Rod Mill Power Draft

Rod mill power is dependent on mill capacity and work index.

Mill power increases with:

  • Increasing rod charge;
  • Increasing mill speed;
  • Increasing mill length.

Rowland and Kjos (1980) provided an expression to quantify power draw at the pinion shaft per unit mass of rods:

P↓M / M↓R = 1.752 D↑0.33 (6.3 – 5.4J↓R) Φ↓C kW/t

D = mill inside diameter (meters)

JR = fraction of mill volume occupied by rods

Φc = fraction of critical speed.

The Rowland and Kjos equation indicates that power draw is a function of the fraction of the critical speed for the mill.

Marcy mills are recommended to operate a peripheral speeds governed by the following relationship :

Peripheral Speed= 108.8 D0.3    meters/ min

D = mill diameter in meters

The Marcy expression is applicable for mill diameters between 1.52 to 4.1meters.

Using peripheral speed, the rotational speed can be determined.

Bond quantified the rod mill power draw as a function of the Work Index, capacity, and a series of correction factors:

PM = Wmtest,i FT Q

FT = F1 F2 F3 F4 F5 F6



Rod Mill Draft Power Corrections

F1 :  Correction for Dry Grinding = 1.1 to 2.0

  • For most materials, F1 = 1.3


F2: Correction for Mill Diameter

F↓2 = (2.44 / D) ↑0.2   for D<3.81 meters

= 0.914   for D>3.81 meters

F3: Correction of Oversize Feed

  • Austin et al. (1984) defined the need for correction when:
    F↓80>4000(14.3/W↓i,test) ↑0.5
  • The optimum top size for a rod mill is defined by:
    F↓opt = 16000(14.3 / W↓i) ↑0.5
  • Correction:
    F↓3 – 1+(W↓i / 1.1 – 7) (F↓80 – F↓opt / F↓opt) /R

F4: Correction for Fineness of Grind

F↓4 = P↓80 + 10.3 / 1.145 Ρ↓80

F5: Correction for Reduction Ratio (low or high)

  • The correction is not needed if:
    -2 < (R – R*) < =2

R↑* – 8 + 5 L↓R / D
Where LR = length of rod in meters

  • Correction
    F5 – 1 + 0.0067 (R – R*)2
Condition Correction
Feed prepared by open circuit crushing 1.4
Feed prepared by closed circuit crushing 1.2


AMIT 135: Lesson 7 Ball Mills & Circuits


At the end of this lesson students should be able to:

  • Explain the role of ball mill in mineral industry and why it is extensively used.
  • Describe different types of ball mill design.
  • Describe the components of ball mill.
  • Explain their understanding of ball mill operation.
  • Explain the role of critical speed and power draw in design and process control.
  • Recognize important considerations in ball mill selection.

Reading & Lecture

  • In ball mills, steel balls or hard pebbles to break particle based on impact and attrition.
  • A rotating mill charged with media and ore is lifted against the inside perimeter.
  • Some of the media falls and impacts the ore particles at the bottom of the mill.
  • The rest of the media cascades and, in the process, creates particle breakage by attrition.
  • The process is continuously repeated as the particles move by mass and volume action through the mill.
  • Dry and wet grinding common.


Ball mill
Ball mill photographed by Ron Frisard and shared on Flickr, CC – Some rights reserved


Mill Type Overview

  • Three types of mill design are common.
  • The Overflow Discharge mill is best suited for fine grinding to 75 – 106 microns.
  • The Diaphram or Grate Discharge mill keeps coarse particles within the mill for additional grinding and typically used for grinds to 150 – 250 microns.
  • The Center-Periphery Discharge mill has feed reporting from both ends and the product discharges from the center bottom.
  • In all systems, the feed trunnion is smaller than the discharge trunnion to ensure a good flow and no backflow to the feed.
Diagram of ball mill and interior cut away
Diagram of ball mill and interior cut away [image: (135-7-2)]


Ball Mill Design Parameters

Size rated as diameter x length.

Feed System

  • One hopper feed
  • Diameter 40 – 100 cm at 30° to 60°
  • Top of feed hopper at least 1.5 meter above the center line of the mill.


  • Single or double helical scoop feeder or a spout feeder
  • Double helical feeders used in closed-circuit with classifiers
  • Spout feeders preferred when using a closed-circuit with classifying cyclones. Cyclones are typically installed above the mill and thus the cyclone underflow is fed to the mill by gravity.

Discharge System

  • One exit unit
  • Exit about 5 – 110 cm lower than the center line of the overflow mill.


Comparison of Tumbling Mill Characteristics

ParameterBall MillRod MillAutogenous Mill
Length: Diameter Ratio1.4 to 1.80.5 to 3.50.25 to 0.50
Feed Size2.5 cm maximum-1.9 cm
-1.25 to 0.9cm
Coarse Ore
Normal Ore
Reduction Ratio15:1 to 20:120:1 to 200:1---



Ball Mill Design

  • A survey of Australian processing plants revealed a maximum ball mill diameter of 5.24 meters and length of 8.84 meters (Morrell, 1996).
  • Autogenous mills range up to 12 meters in diameter.
  • The length-to-diameter  ratios in the previous table are for normal applications.
  • For primary grinding, the ratio could vary between 1:1and 1.8:1.
  • For fine regrinding in open circuit, the ratio ranges from 1.3:1 to 1.5:1.
  • Some ball mills are separated in to compartments by grates. The grates hold back particles above a certain size for additional grinding.
  • The compartments could contain different ball sizes. Large to small from the feed end.
  • Some mills have a conical section. In the conical section near the discharge, fine particles preferentially move into the conical section thereby creating segregation. This type has low feed capacity and is rarely used in the metallurgical industry.



Lifters and Media

Lifters are used on the inside [Periphery of the mill to:

  • Save wear on the steel body;
  • Assist the lift of the media and ore to the desired   height in the mill.

Liners can be made of manganese steel, Ni hard or high carbon steel and hard rubber or synthetic material that is 65 – 75 mm thick.

The liners can be:

  • Smooth
  • Ribbed
  • Waved
  • Double wave liners: 65 – 90 mm above liner thickness
  • Single Wave Liners: 60- 75mm above liner thickness

Liner wear is roughly proportional to rotation speed.


Mill Liners

Mill liners [images: (135-7-4)]
Mill liners [image: (135-7-4)]
Mill liner installation
Mill liner installation [image: (135-7-5)]
Magnetic mill liners
Magnetic mill liners [image: (135-7-6)]


Mill Lifters

The number of lifters generally can be determined by the rule-of-thumb:

Number of Lifters  = 3nD  for double wave liners

= 6.6D for single wave liners where D  is the mill diameter (m).

Double wave liners are more suitable for ball sizes less than 60 mm. Otherwise, single wave is preferred.



Grinding Media

  • The bulk densities of the steel media typically used are:
    Balls  4650 kg/m3   Cylpebs  4700 kg/m3
    Rods  6247 kg/m3    Cubes  5500 kg/m3
  • For soft ore, ceramic  media (90°/o A l203) can be used (2200 kg/m3).


Grinding media
Grinding media [images: mill media (135-7-7)]



Ball Mill Operation

  • Ball mills ride on steel tires or supported on both ends by trunnions.
  • Girth gears bolted to the shell drive the mill through a pinion shaft from a prime mover drive.
  • The prime movers are usually synchronized motors.
  • During rotation, a portion of the charge is lifted along the inside perimeter.
  • After exceeding the angle of repose, part of the charge slides down while part cascades.
Mill motion diagram
Mill motion diagram



Mill Breakage Mechanism

  • According to Morrell (1996), the breakage mechanism is association with media characteristics:
    • Impact Breakage ∞ M↓B↑3  MB = ball mass
    • Attrition Breakage ∞ S↓B↑3   SB = ball surface area
  • The energy of impact will depend on height and the angle of impact.
  • The size reduction will depend on:
    • Charge characteristics (mass, volume, hardness, density, size distribution);
    • Grinding media characteristics (mass, density, number, ball size distribution);
    • Speed of mill rotation;
    • Slurry density when wet grinding



Charge Volume

  • Mill should not be overcharged or undercharged
  • Overloading tends to accumulate fines at the toe of the mill which results in a cushioning effect.
  • When the rock load is low, excessive ball-to-ball contact retards the rate of breakage.
  • The fraction of mill volume occupied by the ore, J↓R:
    J↓R=M↓R / ρ↓S / V↓M x1 / 1–φ   MR = rock mass
    φ = porosity of charge bed
  • The percent of mill volume occupied by grinding media, J↓B:
    J↓R = M↓R / ρ↓S / V↓M x1 / 1–φ   MB – ball media mass
    φB = density of ball media



Charge Height

  • Measurement of charge height is a convenient method to estimate charge volume.
  • Generally :
    • For overflow ball mills, the charge should not exceed 45% of the mill volume .
    • For grate discharge mills, the charge should occupy about 50% of the mill volume .
  • Bond developed a relationship that can be used to determine the percent charge by volume as a function of the vertical height above the charge, He, and the radius of the mill, R, i.e.,
    Charge% = 113-(63HC/R)
  • However, Morrell identified significant errors from this estimate when using small media sizes.


Image of a charged ball mill
Charged ball mill [image: (135-7-9)]


Medium Charge Volume Fraction

  • The fraction of the mill volume occupied by the mill charge can be estimated based on a ratio of the cross-sectional areas.
  • The cross-sectional area of the mill charge (AC) can be determined from:
    A↓C = H↓B / 6W (3H↓B↑2 + 4W↑2)
  • Since the cross-sectional area of the mill is simply πR2, the mill volume fraction occupied by the media charge is:
    J↓B = A↓C / πR↑2 – H↓B / 6W (3H↓B↑2 + 4W↑2) (1/πR↑2)
    where W = 2(R↑2 – H↑2) ↑ 0.5


Ball Size as Initial Charge

  • Commercial ball sizes 10 – 150 mm
  • Number, size and mass of each ball size depends on mill load and whether or not the media is being added as the initial charge.
  • For the initial chargin of a mill, Coghill and DeVaney (1937) defined the ball size as a function of the top size of the feed, i.e.,
    d↓V = 0.40 K√F
    dB = ball size (cm)
    F = feed size (cm)
    K = proportionality constant described as the grindability factor

    • Hard ores, K = 37.4;
    • Soft ores, K = 29.8



Ball Size vs. Grindability

It has been recognized that the grindability of an ore in a ball mill is a function of both feed and mill parameters:

  1. Work   index, Wi
  2. Largest particle size and size distribution
  3. Density of solids and slurry
  4. Mill diameter
  5. Rotational speed

Rowland and Kjos (1980) defined the largest ball size needed based on these parameters:

d↓B = 25.4 [(F↓80 / k) ↑0.5 (ρ↓s W↓i / 100φ↓C (3.281 D) ↑0.5) ↑0.33 ]  mm
D = inside diameter of mill (meters)
φC = fraction of the mill critical speed
k = mill factor constant

Mill Factor, k

Mill TypeWet/Dry GrindingCircuitk value



Cylpeds Size

  • Doering International proposed the following expression when cylpeds are used as grinding media
    • d↓B = 18.15 [(F↓80 / k) ↑0.5 (ρ↓s W↓i / 100φ↓C (3.281 D) ↑0.5) ↑0.33 ]   mm
  • When the estimated ball size is less than 25mm or the cylpeds size is less than 22 x 22 mm, it is estimated that the size should be increased 20% to 30%.


[images: (135-7-10)]


Ball Mill Size as a Replacement

  • Grinding media wears and reduces in size at a rate dependent on the surface hardness, density and composition of the ore.
  • Ball wear is directly proportional to surface area per unit mass and thus inversely proportional to ball diameter.
  • Other factors include:
    • Speed of mill rotation;
    • Mill diameter;
    • Mineral density;
    • Work Index.
  • Bond estimated the amount of wear in terms of kilograms per kWh based on the abrasion index, A;, i.e.,
    • Wet Ball Mill = kg  kWh = 0.16(Ai -0.015)0.33
    • Dry Ball Mill = kg / kWh = 0.023Ai 0.5

Replacement Ball Size

  • Rowland and Kjos proposed the use of their equation for the determination of the initial and replacement media size.
  • Azzaroni (1981) and Dunn (1989) recommended the use of the following expression for the size of the makeup media:
    d↓B – 6.3(F↓80) ↑0.29 (W↓i) ↑0.4 / (νD) ↑0.25Where ν = the rotational speed of the mill.

Ball Bulk Density

  • Low density media can be used for soft and brittle materials.
  • Hard materials required high density media.
  • Rose and Sullivan (1961) estimated the required media density (ρB) using the expression:
    ρ↓B = (0.016ρ↓S↑2 + 20ρ↓S↑2) ↑0.5 – 0.4ρ↓s
  • Cast iron (ρB = 4.3 – 4.8) and forged steel (ρB = 4.6 – 4.8) are common materials used for media.
  • Tungsten carbide media is used for very abrasive and hard ores (ρB = 14.9).
  • Pebbles and ceramic media (ρB = 3.6) are adequate for soft materials.

Ball Size Distribution

  • As the mill starts, grinding action and throughput increases.
  • However, after reaching a critical speed, the mill charge clings to the inside perimeter of the mill.
  • Under this conditions, the grinding rate is significant reduced or stopped.
  • All mills must operate less than Critical Speed
  • At position A, the media is held to the wall due to the following force balance:
    Mg cosθ = Mν↑2 / (R – r)g

    • R = Mill radius
    • ν = linear mill velocity (m/s)
    • M = Ball mass
    • r = ball diameter
    • g = gravitational acceleration
Ball size distribution diagram
Ball size distribution diagram [image: (135-7-11)]

Critical Rotational Speed

  • At θ=0° and cos θ = 1, the gravitational force pulling the media off the mill was maximized.
  • Substituting and solving for speed rotational provides the expression for quantifying the critical velocity, vc:
    ν↓C = 42.3 / √(D-d)  revs/min
  • The above equation assumes no friction between the media and the liner.
  • In practice, friction decreases with:
    • Smoothness of liner
    • Fineness of media
    • Pulp density
    • Abrasiveness of the material to be ground
  • To modify the critical speed to account for friction:
    • For dry grinding, multiply by 0.65.
    • For wet grinding, multiply 0.70.
Critical rotational speed
Critical rotational speed [image: (135-7-12)]

Mill Speed Impact on Optimum Breakage Condition

% Critical SpeedSlidingCascadingCentrifuging

*Nordberg, 1970

Optimum speed to maximize impact breakage is 70% to 80% of critical speed.

Ball Charge Impact on Optimum Breakage Condition

Ball Charge %
by Volume
(all speeds)
15-2531 (high speeds)---
25-3522 (high speeds)1 (high speeds)
35-4513 (all speeds)1 (high speeds)
45-5012 (all speeds)3 (all speeds)

*Nordberg, 1970

Optimum ball charge to maximize impact breakage is 35% to 45% of critical speed.

Mill Throughput Capacity

Mill capacity is a function of:

  • Mill dimensions
  • Type of mill
  • Mill speed
  • Mill loading
  • Required particle size
  • Feed size
  • Work Index
  • Mill shaft power
  • Specific gravity of the rock

Bond developed an expression for capacity that accounts for each of these factors.

Ball Mill
A ball mill in situ and operating in Alaska.

Mill Throughput Capacity

  • Bond expressed mill capacity as a function of mill shaft power (PM, kW) and the energy required for particle breakage (kWh/f):Q = P↓M / E
  • The expression for mill shaft power developed by Bond incorporates a number of operating parameters,P_{M} = 7.33 J_{B} \phi_{C} (1 - 0.937 J_{B}) \rho _{B}LD^{2.3}\left ( 1 - \frac{0.1}{2^{9-10_{\phi C}}} \right )
  • The energy required for breakage was previously discussed, i.e.,E = W↓I(10 / √P↓80 – 10 / √F↓80
    WI must be adjusted for nonstandard conditions


Mill Throughput Capacity (Austin et al., 1984)

  • Austin et al. concluded that a single expression for capacity is not adequate for all mills.
  • Equations for mill sizes less than 3.81meters in diameter and greater than 3.81meters were proposed:
    • Q = \frac{6.13D^{3.5}(\frac{L}{D})\rho _{B}(J_{B} - 0.937 J_{B}^{2})(\phi _{C} - \frac{0.1\phi _{C}}{2^{9-10 \phi_{C }}})}{C_{F}W_{i, test}10\left ( \frac{1}{\sqrt{P_{80}}} - \frac{1}{\sqrt{F_{80}}} \right )}   t/h   D < 3.81 m
    • Q = \frac{8.01D^{3.3}(\frac{L}{D})\rho _{B}(J_{B} - 0.937 J_{B}^{2})(\phi _{C} - \frac{0.1\phi _{C}}{2^{9-10 \phi_{C }}})}{C_{F}W_{i, test}10\left ( \frac{1}{\sqrt{P_{80}}} - \frac{1}{\sqrt{F_{80}}} \right )}   t/h   D > 3.81 m
  • The factor CF is the correction for non-standard conditions including wet open circuit, wet closed circuit, wet and dry grinding, over size feed and under size grinding.

Mill Power Draw

  • The motor power draw required to turn a mill from rest to the operating speed includes the energy required for the initial starting torque and mechanical arrangements to rotate the mill.
  • It is generally accepted that practical mill power (PM ) is a function of mill capacity and diameter, i.e.,PM = Mill Constant * (Mill Diameter )n
    where n = 0.3 to 0.5.
  • It is evident that mill power is a function of the height at which the media is lifted and the density of the media, i.e.,

    M = K ρb LD2.5where k is a proportionality constant.


Mill Power Draw (Bond Method)

Based on a large number of observations, power draw was determined to be:

  • Directly proportional to the mill length;
  • A function of mill speed;
  • A function of the total mass of the grinding media and rock charge;
  • A function of the feed characteristics;
  • A function of the work index of the material.

Bond developed an express ion to quantify mill shaft power based on data from a number of laboratory and industrial ball mills:

P↓S = 7.33J↓B Φ↓c (1-0.937J↓B)ρ↓b LD↑2.3 (1-0.1 / 2↑9 – 10Φ↓C)

ρS = Mill power

D = Mill diameter in meters

L = Mill length in meters

ρB = Ball density in t/m3

Wet Ball Mill Power Draw (Bond)

  • For wet ball mills, Bond expressed power draw as a function of the total mass of media:P↓M / M↓B – 15.6Φ↓V (1 – 0.937 J↓B) D↑0.3 (1 – 0.1 / 2↑9 – 10Φ↓C) kW/t
    M↓B = πD↑2 / 4 J↓B ρ↓B (1 – Φ)
  • The bed porosity is typically in the range of 35% to 40%.
  • In practice, the mill shaft power for wet overflow mills calculated using the above expression appeared to overestimate the actual power when:
    • Maximum ball size, dmax < 45.7
    • Mill inside diameter > 2400mm

Bond Wet Overflow Mill Corrections

  • Corrections to counter the over estimation included in a slump factor, Fs:F↓S = 1.102 (45.72 – d↓max / 50.8) kWtThe Fs factor is subtracted from the calculated power draw.
  • The ball size factor, FB, is added to the mall shaft power for mill sizes greater than 3.3 meters:F↓B – 1.102 (d↓max – 12.5D / 50.8) kW/t

Other Rowland & Kjos Power Draw Corrections

  1. F1 : Dry grinding correction
  2. F2 : Correction for wet open circuit since it requires more power than wet closed circuit.Based on the sieve size used to determine the work index and the percentage of the product passing this size.
    Power Draw Corrections
    Power Draw Corrections [image: 135-7-14)]
  3. F3: Correction for material in the feed that is greater than the optimum size, F0S:
    F↓0S = 4000[13 / W↓I] ↑0.5
    F↓3 = 1+1 / R[W↓i – 7] [F↓80 / F↓0S – 1]
  4. F4: Correction when the product size is less than 75 microns:
    F↓4 = [P↓80 + 10.3 / 1.145P↓80]
  5. F5: Correction when the reduction ratio is less than 6:
    F5 = 1+0.13 / (R – 1.35)


Mill Dimension Design

  • Ore: limestone
  • Throughput: 250 Tph
  • F80 = 10mm
  • P80 = 0.1mm

Calculate the mill size required to handle the desired throughput:


W = 10*11.25(1/√100 – 1/√100 0) kWt/t = 10.125 kWh/t

Mill Dimension Design Example

Example: PM = 250 * 10.125 = 2531 kW

The Nordberg Method: PM = 2.448 ABCL


  • A = Mill diameter factor
  • B = % charge loading factor
  • C = mill speed factor
  • L = Length of mill
Nordberg Factor A Diagram
Factor A Diagram [image: (135-7-15)]
Factor B Diagram
Factor B Diagram [image – (135-7-16)]
Factor C Diagram
Factor C Diagram [image: (135-7-17)]


Mill specs for design
Mill specs for design [image: (135-7-18)]

Mill Power Consumption Example

  • Ball mill = 3.5 m x 3.5 m
  • Rubber lining = 75 mm
  • % Mill volume charge = 40%
  • Grinding balls diameter = 70 mm
  • Mill operational speed = 17.6

Calculate the optimum power consumption to operate the mill.


P↓M / M↓B = 15.6Φ↓C (1 – 0.937 J↓B) D↑0.3 (1 – 0.1 / 2↑9-10Φ↓C) kWt

M↓B = πD↑2 / 4 J↓B ρ↓B (1 – Φ)


  • Actual mill diameter = 3.5-2 * 0.075 = 3.35
  • Critical Speed
    • ν↓C = 42.3 / √(D-d) rpm = 23.4
  • ΦC = (17.6 / 23.4_ * 1000 = 0.75
  • PM / MB = 10.14 kW/t
  • With ball density = 7.8 t/m3
    • MB = 57.75 t
  • Slump correction factor check:
    • D > 2.4 m but d > 45.7 mm, so no slump correction required
  • Ball size correction factor check:
    • D > 33.3 m,  so a ball size correction factor should be applied
      F↓B = 1.102 (d↓max – 12.5D / 50.8) kWt/t = 0.010 kW/t
  • So corrected PM / MB = 10.14 + 0.610 = 10.75 kW/t
  • Total power – 10.75 kW/t * 57.75 t = 621 kW


























AMIT 135: Lesson 6 Grinding Circuit


At the end of this lesson students should be able to:

  • Explain the grinding process
  • Distinguish between crushing and grinding
  • Compare and contrast different type of equipment and their components used for grinding
  • Identify key variables for process control
  • Design features of grinding equipment (SAG, BALL and ROD MILLS)
  • Explain typical flowsheets of grinding circuits involving single or combination of equipment

Reading & Lecture

Size reduction by crushing  has a size limitation for the final products. If further  reduction is required, below 5- 20mm, grinding  processes should be used.

Grinding is a powdering or pulverizing process using the rock mechanical forces of impaction and attrition.

The two main objectives for a grinding  process are:

  • To liberate individual minerals trapped in rock crystals (ores) and thereby open up for a subsequent enrichment in the form of separation.
  • To produce fines (or filler) from mineral fractions by increasing the specific surface.

Grinding takes place in more “open” space which makes the retention time longer and adjustable compared to crushers.

Chart showing theoretical size reduction and power ranges for different grinding mills
Theoretical size reduction and power ranges for different grinding mills
[image: (135-6-1)]

AG/SAG Mills

Autogenous Grinding (AG) Mill

  • Wet or dry
  • Primary, coarse grinding (up to 400 mm feed size)
  • Grinding media is grinding feed
  • High capacity (short retention time)
  • Sensitive to feed composition (critical size material)

Semi-Autogenous Grinding (SAG) Mill

  • Wet or dry
  • Higher capacity than A-G mill grinding
  • Primary, coarse grinding (up to 400 mm feed size)
  • Grinding media is grinding feed plus 4-12% ball charge (ball dia.100- 125 mm)
  • High capacity (short retention time)
  • Less sensitive to feed composition (critical size material)

Semi-Autogenous Mill

An image of a very large ball mill
Note the size of the mill: Why does the diameter need to be so big?
[image: (135-6-2)]

SAG Mill Circuit Example – Gold Processing

SAG mill circuit example for gold processing
SAG mill circuit example for gold processing
[image: (135-6-3)]


  • AG/SAG  mills are normally used to grind run-off-mine ore or primary crusher product.
  • Wet grinding in an AG/SAG  mill is accomplished in a slurry of 50 to 80 percent solids.
Image of a simulation of a charged ball mill
2D and 3D simulations of particles in a SAG Mill
red=fastest, blue=slowest moving particles
[image: (135-6-4)]

  • The mill product can either be finished size ready for  processing, or an intermediate size ready for final grinding in a rod mill, ball mill or pebble mill.
  • AG/SAG mills can accomplish the same size reduction work as two or three stages of crushing and screening, a rod mill, and some or all of the work of a ball mill.
  • Because of the range of mill sizes available, AG/SAG milling can often be accomplished with fewer lines than in a conventional rod mill/ball mill circuit.
A diagram of types of AG/SAG mills
A diagram of types of AG/SAG mills
[image: (135-6-5)]


Types of rod mills
A diagram of types of rod mills [image: (135-6-6)]

Rod Mills

  • Wet only
  • Coarse grind
  • Primary mill at plant capacities of less than 200 t/h
  • Coarse grinding with top size control without classification
  • Narrow particle size distribution
  • Mostly dry
  • Coarse grind high capacity
  • Special applications
  • End discharge: finer product
  • Centre discharge: rapid flow, less fines
  • Narrow particle distribution

Grate discharge is not available in Rod Mills


Rod mills in situ
Rod mills in situ
[image: (135-6-7)]

Rod Mill Comparison


Rod mill diagrams of overflow and grate discharge
Rod mill diagrams of overflow and grate discharge
[image: (135-6-8)]


  • Wet only
  • Robust and simple
  • Finer grind (longer retention time)
  • High risk for over grinding
  • Ball charge 35-45%


  • Discharge end more complicated
  • Coarser grind (shorter retention time)
  • Lower risk for over grinding
  • Can take about 5-10% more ball with corresponding higher throughput
Images of a ball mill exterior, interior, and grinding media
Ball mill exterior, interior, and grinding media
[image: (135-6-11)]


Pebble Mill

A pebble mill diagram
Pebble mill diagram
[image: (135-6-13)]
  • Wet or dry
  • Always grate discharge
  • Secondary grinding
  • Grinding media :
    • A size fraction screened out from feed
    • Flint pebbles
    • Porcelain balls
    • Al203 balls
  • Larger than Ball mills at same power draw


Special Tumbling Mill

Special tumbling mills
Special tumbling mills
[image: (135-6-14)]
Conical Ball Mill

  • Wet or dry (air swept)
  • Overflow or partial grate
  • Conical shell for “graded” ball charge and optimal size reduction
  • Only available in small and intermediate sizes
  • Efficient “high reduction ratio grinding”
SSR Mill (Svedala Rubber Roller mill)

  • Wet or dry
  • Overflow and grate discharge
  • Light and fabricated construction
  • Ready assembled on steel frame
  • Easy to move
  • Limited in size (max. diameter 2.4 m)

Vertimill® (Metso Minerals)

  • Wet grinding only
  • Top or bottom feed
  • Grinding by attrition/abrasion
  • Primary or regrinding mill
  • Ideal for “precision” grinding on finer products
  • Restriction in feed size (6mm)
  • Restriction in energy (1119 kW/ 15oo hp)
  • Ball size max. 30mm
Vertimill diagram
Vertimill by Metso Minerals
[image: (135-6-16)]

Stirred Mills vs. Tumbling Mills

Advantages of Stirred Mills (VERTIMILL®):

  • Lower installation cost
  • Lower operation cost
  • Higher efficiency
  • Less floor space
  • Simple foundation
  • Less noise
  • Few moving parts
  • Less overgrinding
  • Better operation safety

Typical Cost of Grinding

  • The main costs for grinding are energy, liners and grinding media.
  • They are different for different mill types. For tumbling mills:
Diagram of cost breakdown by mill type
Diagram of cost breakdown by mill type
[image: (135-6-17)]


Basic Mill Linings

  • Use rubber linings wherever possible due to lifetime, low weight, easy to install and noise dampening.
  • When application is getting tougher use steel-capped rubber, still easier to handle than steel.
  • When these both options are overruled (by temperature, feed size or chemicals) use steel.
  • Ore-bed is a lining with rubber covered permanent magnets used for special applications like lining of VERTIMILLs, grinding of magnetite
Three images of different types of lining types
Various types of mill linings
[image: (135-6-18)]


Size Grinding Mills

Fundamental to all mill sizing is determining the necessary specific power consumption for the grinding stage (primary, secondary, tertiary etc.) .

It can be established (in falling scale of accuracy) in one of the following ways :

  1. Operating data from existing mill circuit (direct proportioning) .
  2. Grinding tests in pilot scale, where the specific power consumption is determined (kWh/t dry solids) .
  3. Laboratory tests in small batch mills to determine the specific energy consumption.
  1. Energy and power calculations based on Bonds Work Index (Wi, normally expressed in kWh/ short ton).
  2. Other established methods, for instance Hardgrove Index, population balance.



Scale Up in Sizing for Grinding Mills

  • Scale-up criterion is the net specific power consumption, i.e. the power consumed by the mill rotor itself minus all mechanical and electrical losses divided by the feed rate of solids.
  • For the full scale mill, specific power is multiplied by the feed rate to get the net mill power. This must then be increased by the anticipated mechanical inefficiencies (bearing/gear friction losses and possible speed reducer losses) as well as electrical losses, in order to arrive the gross mill power.
  • For all AG or SAG installations, batch lab tests are mandatory to determine whether this type of grinding is possible at all, as well as establishing the necessary specific power consumption.



Size Reduction Circuits

Single Stage AG Mill

For the rare cases where primary AG milling will inherently produce the required product size. (Wet and dry)

AG Mill + Crusher

For the cases where critical size fractions needs to be removed from the mill and crushed separately to prevent overgrinding. Resulting size must match product requirements.

Single stage AG mill and AG mill with crusher circuits
[image: (135-6-19)]



AG Mill + Ball Mill + Crusher (ABC Circuit)

  • This can be used to correct a too coarse product from the   primary mill.
  • Mostly operated wet, but also dry possible.

AG Mill + Pebble Mill

  • Two stage AG-grinding with the primary mill in open circuit and the secondary pebble mill in closed circuit.
  • The pebbles screened out from the primary mill or recirculated to the primary mill based on size.
Circuits diagramming AG mill and Ball Mill and Crusher as well as AG Mill, and Pebble Mill
Circuits diagramming AG mill + Ball Mill + Crusher as well as AG Mill + Pebble Mill
[image: (135-6-21)]



AG Mill + Ball Mill / Vertimill

  • Pebble mill is replaced by a ball mill or a Vertimill in the previous circuit.
  • This is used when there is not enough pebbles available in the circuit, or all autogenous grinding produces too much fines

AG Mill + Ball Mill / Vertimill

  • Pebble mill is replaced by a ball mill or a Vertimill in the previous circuit.
  • This is used when there is not enough pebbles available in the circuit, or all autogenous grinding produces too much fines
Two circuits diagramming AG Mill and Ball Mill / Vertimill
Circuits diagramming AG Mill + Ball Mill / Vertimill
[image: (135-6-23)]



Single Stage SAG Mill

  • Using SAG instead of AG increases the capacity as well as application range, but will also increase wear costs and still be dependent on “natural” product size being close to the desired.
  • Common circuit in the US and Canada


Single stage SAG mill circuit
Single stage SAG mill circuit
[image: (135-6-25)]

Closed Vertimill Circuit with Integral Classifier

  • Used for wet circuits with not too fine desired product and/or not stringent coarse end oversize of the product.
  • Max. feed size – 6 mm (1/4″).



Closed Vertimill circuit with integral classifier
Closed Vertimill circuit with integral classifier
[image: (135-6-26)]








AMIT 135: Lesson 5 Crushing

AMIT 135: Lesson 5 Crushing


At the end of this less students should be able to:

  • Explain the need for crushing operation
  • Define terminologies involved in crushing operation
  • Explain how crushing works
  • Explain the stages involved in crushing operation (Primary, Secondary and Tertiary)
  • Recognize different types of crushing equipment used in Mineral industry
  • Compare different equipment components and different methods to control the crushing process

Reading & Lecture

The Art of Crushing

Crushing Gravel & Rock

  • Limited size reduction
  • Cubical shape
  • Over and undersize important
  • Flexibility
  • For gravel: less crushing, more screening
  • For rock: crushing and screening

Crushing Ore

  • Maximum size reduction
  • Shape of no importance
  • Over and undersize of minor importance
  • Flexibility of minor importance
  • More crushing, less screening
  • Low production costs, high utilization



Crushing of Ore and Minerals

  • Normally the size reduction by crushing is of limited importance besides the top size of the product going to grinding.
  • This means that the number of crushing stages can be reduced depending on the feed size accepted by primary grinding stage.
Image of a "Classical" 3-stage ore crushing prior to rod mill
Image of a “Classical” 3-stage ore crushing prior to rod mill [image: (135-5-1)]
Diagram of Typical 1-2 stage ore crushing prior to AG-SAG mill
Diagram of Typical 1-2 stage ore crushing prior to AG-SAG mill [image: (135-5-2)]

Calculation of Reduction Ratio in Crushing

Calculation of reduction ratio in crushing
Calculation of reduction ratio in crushing [image: (135-5-3)]


Crushing Equipment

  • The selection of the right crushing equipment is influenced by many factors some of which are upstream of the crushing plant (e.g. blasting pattern and mining method) and others which are downstream of the crushing plant (e.g. mill and grinding circuit selection).
  • Crushers have more efficient transfer of applied power to the breakage of rock than grinding mills.
  • Typically a crushing flowsheet for a mineral processing plant will have from one-to-three stages of crushing. There are some cases where the process requires a fine dry product and a quaternary stage of crushing will also be included.


Primary Crushing

  • The purpose of the primary crusher is to reduce the ROM ore to a size amenable for feeding the secondary crusher or the SAG mill grinding circuit.
  • The ratio of reduction through a primary crusher can be up to about 8:1.
  • Feed:
    • ROM up to 1.5 m
  • Product:
    • -300mm (for transport) to -200mm (for SAG mill)
  • Feed Rate:
    • 160 to 13,000 tph
  • The family of primary crushers include:
    • Gyratory Crushers
    •  Jaw Crushers
    •  Impact Crushers
  • Typical rules for primary crusher selection:
    • Rule 1: Always use a jaw crusher if you can due to lower costs.
    • Rule 2: For low capacity applications, use jaw crusher and hydraulic hammer for oversize.
    • Rule 3: For high capacities, use jaw crusher with big intake openings.
    • Rule 4: For very high capacities, use gyratory crusher.



Jaw Crusher

  • Crushing occurs between two moving plates that are arranged to form an acute angle to apply a compressive force that results in tensile failure
  • Typically preferred for feed rates of 900 tph or less.
  • Can be located underground or surface
  • Typically only a primary crusher.
  • Operated in open circuit
  • The gape and the width are set values for a given crusher while the setting can be altered to adjust the product size.
Diagram of a jaw crusher
Diagram of a jaw crusher [image: (135-5-4)]
A diagram of a jaw crusher
Diagram of a jaw crusher [image: (135-5-5)]


Single Toggle Jaw Crusher

  • The maximum motion is at the top of the jaw.
  • Light to medium duty crusher and capable of crushing ores up to 200 Mpa (27.500 psi)
Diagram of a single toggle jaw crusher
Diagram of a single toggle jaw crusher [image: (135-5-6)]



Double Toggle Jaw Crusher

  • The maximum motion is at the bottom of the jaw
  • Capable of crushing ores up to 350 Mpa (90,000 psi)
Diagram of a double-toggle jaw crusher
Diagram of a double-toggle jaw crusher [image: (135-5-7)]



The dimensions defined by those particle sizes are:

  • Gape: The distance between the jaws at the feed opening
  • Closed side set (CSS): The minimum opening between the jaws during the crushing cycle (minimum discharge aperture)
  • Open side set (OSS): The maximum discharge aperture
  • Throw: The stroke of the swing jaw and the difference between OSS and CSS.
A diagram of a jaw crusher
Diagram of a Jaw Crusher
[image: (135-5-9)]



Jaw Crusher Fundamentals

  • Vertical Height = 2 x Gape
  • Width of Jaw  > 1.3 x Gape
    < 3.0 x Gape
  • Throw = 0.0502 (Gape) 0.85
  • Gape is measured in meters.
An animated jaw crusher diagram
Jaw crusher action




Jaw Crusher Sizes and Power Ratings

  • Size is specified in terms of the gape and width, typically listed as gape x width.
  • Largest jaw crusher is 1600 x 2514 mm with motor ratings of 250-300 kW.
  • Metso crushers (C200 series) are 1600 x 2514 mm with motors rated at 400 kW.
  • The largest particle that can enter the opening of the jaw crusher can be estimated by:

Largest particle size= 0.9 x gape

  • The largest particle to report to the jaw crusher is typically defined by the drilling pattern in the mine.


Typical Jaw Crusher Characteristics

Jaw Crusher Size (mm) Reduction Rate Range Power (kW)
Gape Width Min Max
Min Max Min Max
Double Toggle 125 1600 150 2100 4:1-9:1 2.5 225
Single Toggle 125 1600 150 2100 4:1-9:1 2.5 400

Toggle Speed:

  • maximum = 300 rpm
  • minimum = 100 rpm


Jaw Crushers (Metso Minerals)

Jaw Crusher Specifications

TypeH mm (inch)L mm (inch)W mm (inch)Weight (ton)KW/hp
Max Power
C631600 (63)1950 (77)1390 (55)6.0545/60
C801700 (67)2020 (80)1565 (62)7.5275/100
C1002400 (95)2880 (113)2250 (89)20.10110/150
C1052050 (81)2630 (104)1920 (76)13.50110/150
C1102670 (105)2830 (112)2385 (94)25.06160/200
C1252900 (114)3370 (133)2690 (106)36.70160/200
C1403060 (121)3645 (144)2890 (114)45.30200/250
C1453330 (131)3855 (152)2870 (113)53.80200/250
C1603500 (140)4200 (165)3180 (125)68.60250/300
C2004220 (166)4870 (192)3890 (153)118.40400/500
C30552400 (95)2920 (115)2550 (100)25.50160/200
Feed Top Size Chart
Feed top size chart [image: (135-5-11)]
Jaw crusher diagram
Jaw crusher diagram [image: (135-5-12)]

Closed-Side Setting Effect on Feed Size

Measurement of the crusher’s closed side setting (CSS) varies depending on the jaw profile that is being used and has an impact on the crusher’s capacity and product gradation.

Diagram of closed-side setting effect on feed size
Diagram of closed-side setting effect on feed size [image: (135-5-13)]

Feeding Jaw Crushers

  • It is desirable to feed jaw crushers continuously.
  • However, feed is often provided intermittently using front end loaders, shovels or trucks.
  • When the feed rate exceeds the product rate, the condition is known as choke feeding.
  • In choke feeding, particle breakage occurs between the plates and particles and between the particles themselves.
  • Choke feeding produces fines; desirable for liberation purposes.


Typical Jaw Crusher Operation

  • Product size is smaller than the open side setting.
  • Typical operating and performance characteristics:
Top Feed Size = 0.8- 0.9 x Gape
Reduction Ratio = 4:1 to 7:1
Throw = 1 – 7em
Speed = 100 – 359 rpm
Frequency of Stroke = 100 – 300 cycles/minute



Jaw Crusher Capacity

  • Capacity is primarily a function of:
    • crusher design characteristics such as width and depth of crushing chamber.
    • open and closed side settings.
    • options on feeding method, intermittent or continuous.
    • operating characteristics like the length of stroke, the number of strokes per minute, and the nip angle.
  • Mathematically, capacity can be represented by the expression:
    Q = f(w,L,L_{max},L_{min},L_{T},n, K,\theta )


w = width Lr – length of stroke
L = height n = frequency (rpm)
Lmax = open side setting K = machine characteristic constant
Lmin = closed side setting θ – jaw angle



Critical Jaw Crusher Parameters

A diagram of jaw crushers
A Diagram of Jaw Crushers [image: (135-5-14)]


Frequency Effect on Capacity
  • Rose and Hill (1967) considered crusher capacity by determining the amount of time and distance a particle takes between two jaw plates.
  • Particles in the A-B zone discharges at the next reverse movement of the jaw.
  • The maximum size of a particle dropping out of the crusher dmax is determined by the open size setting (Lmax).
  • The rate at which the crushed particles move through the crusher is a function of the cycle frequency, υ.
  • Rose and Hill (1967) recognized that the capacity of a jaw crusher increases with frequency up to a maximum and then decreases with a further increase in frequency.
  • Above a critical frequency υc, the particles are unable to move downward a distance h during each cycle.
  • Rose and Hill derived an expression for quantifying the critical frequency value.
  • At this frequency, the maximum capacity is realized.


Jaw Crusher Advantages

  • Lower installed cost than gyratory crushers.
  • Can handle high abrasion with low maintenance.


Jaw Crusher Disadvantages

  • Maximum capacity of 1,000 MTPH.
  • Can be used for primary crushing only.



Gyratory Crushers

  • Invented by Charles Brown in 1877 and developed by Gates in 1881; Gates Crusher.
  • A conical element is supported in a flared shell or frame creating a chamber wide at the top and narrow at the bottom.
  • The center element is caused to gyrate about its fulcrum point causing it to advance and retreat with relation to the shell.
  • Rock introduced at the top is broken as it passes through the crusher chamber.
  • Typical Capacities:
  • Reduction Ratio = 3:1 to 10:1
  • 300 to 9100 tph



Gyratory Crusher History

Gyratory Crusher History
Gyratory Crusher History [image: (135-5-15)]


Gyratory Crusher Dimensions

  • Breaking head (mantle) is fixed to a central spindle which is suspended from a spider hydraulically or mechanically.
  • Bottom end of the spindle is connect to a bevel and pinion arrangement.
  • Primarily compressive breakage.
  • Tolerates different particle shapes including slabby rock.
  • Dimensions :
    • For sizes < 66cm, the circumference along the opening = 8-10 x Gape
    • For sizes > 66cm, the circumference = 6.5 x 7.5 x Gape.
    • Mantle diameter to Gape = 1.3-1.7:10.
    • Feed size= 0.9 x Gape
  • Angle of nip varies for large crusher between 21°to 24°. For curved surfaces, the nip varies from 27° to 30°.
  • The distances between the concave surface and the mantle on top and bottom are usually used to describe the size of the crusher.
  • Other characteristic identifications:
    • Bowl diameter at the discharge x Gape
    • Bowl diameter at the feed end x Gape
    • Bowl circumference at the feed end x Gape
    • Maximum diameter at the head x Gape.


Diagram of a gyratory crusher
Diagram of a gyratory crusher [image: 135-5-16)]

Gyratory Crushing Action

  • Designs of the breaking faces vary with manufacturer.
  • As a result, the product size distribution varies.
  • When the feed drops into the crusher, the mantle squeezes the rock against the concave surface.
  • When the mantle moves away and the rock drops down further and subject to additional crushing during the next cycle .
  • Material exits the crusher through the open side setting.
  • Thus, the top size of the product is determined by the open side setting.
Vertical view of gyratory crushing
Vertical view of the crushing action [image: (135-5-17)]

Long Shaft Gyratory (generally, not used commercially)

Size, mm63 - 7111829 - 2294
Set Range25.4 - 44.5228 - 305
Power, kW2.2298



Short Shaft Gyratory

Size, mm762 - 15242133 - 2794
Set Range50.8 - 152178 - 305
Power, kW149750



Gyratory Design Characteristics

TypeH mm (inch)W mm (inch)Weight (ton)
Max Power
S 42-654807 (189)3937 (155)119.4375/502
S 48-745915 (233)4597 (181)248.0450/603
S 54-755915 (233)4928 (194)248.0450/603
S 60-897169 (282)6299 (248)570.0750/1006
Gyratory design specification
Gyratory Design Specifications
[image: (135-5-18)]

Gyratory Circuit Design

  • Large units are rarely installed underground.
  • Charge is fed by trucks, tip-wagons, side dump cars, and conveyor belts.
  • Feed enters from a hopper and passes through a grizzly screen to remove oversize
  • Gyratory crushers are operated in open circuit.
  • The feed is limited to 1 to 1.5 meters in size.
  • Thus, based on reduction ratio, the rock size is reduced to 10 to 15 cm.
  • Typical reduction ratios are:
    • Primary crusher: 3:1 to 10:1
    • Secondary crusher: 6:1 to 8:1
    • Tertiary crusher: 10:1
      Therefore, if a 3 mm crusher product is required, maximum feed size to the secondary crusher would be 240 mm. Thus, the feed to the primary crusher should not exceed 2400 mm.



Gyratory Operation

  • Performed in dry conditions.
  • Water may be used occasionally for lubrication purposes .
  • Up to 8%-10% moisture feed is acceptable; however, fines should be less than 10%.
  • Performance affected by:
    • Feed fines content (< 10%)
    • Inherent and total moisture content
    • Feed distribution in the crushing area
    • Feed bulk density
    • Hardness of ore (W;)
    • Recirculating load
(Gape x Mantle Dia., mm)
(open side, mm)
(closed side, mm)
Work Index
1219 x 1879200341352200--
1371 x 1879137-223441353100--
1828 x 231119444111275013
1524 x 2268200 - 2753711332006
1524 x 2268238-2753792318012
1219 x 2057175-1883793133010
1524 x 225341342290--



Minimum Gyration Speed

  • The gyration speed determines that rate at which product is generated at the desired particle size .
  • It is also known that gyration speed must be slowed if the particle size of the feed is increased.
  • Friction controls the flowability of the material through the gyratory.
  • Friction values are typically between 0.2 and 0.3 .
  • For a cone angle of 75°, friction of 0.2, and product size of 10.2 cm, the minimum gyration speed is 190 rpm.


60-1101525175-2505575 - 7605



Specific Power Requirements

  • Run-of-mine material contains a range of particle sizes
  • Thus, only the power required to break particles that are greater than the open-side setting should be included in the overall power requirement
  • In actual practice, it has been found that the total power requirement PA is:
    P ↓A = 0.75 Q P
  • This expression is valid for primary crushers. For secondary cone crushers, the 0.75 value takes a value of unity.



Advantages vs. Disadvantages of Gyratory Crushers


  • Designed for direct dump from trucks up to 300 tons.
  • High capacity rating.
  • Lowest maintenance per ton processed .
  • Highest availability.
  • Can handle crushing ore with compressive strength of up to 600 MPa (90,000psi).


  • Highest installed capital cost.




Cone Crushers

  • Originally designed and developed by Symons (1920).
  • Similar to gyratory except the spindle is supported at the bottom of the gyrating cone instead of being suspended.
  • The head to depth ratio is larger than gyratory crushers.
  • Cone angle are flatter and the slope of the mantle and concaves are parallel.
  • The flatter cone angles increase residence time and thus produce finer particles.
  • Shell is held by springs which allow passage of unbreakable rock.
  • Breakage is by impact.


Cone Crusher Diagram
Cone Crusher Diagram [image: (135-5-19)]
Symons Cone Crusher Drawing
Symons Cone Crusher Drawing [image: (135-5-21)]



  • Secondary crushers are typically Standard Head with stepped liners
  • Tertiary crushers are Short head which have smoother crushing faces and steeper breaking head cone angles.

Standard Symons Cone Crushers

Design CharacteristicsOpen CircuitClosed Circuit
Size (mm)30506003050600
Crusher Chamber Size (mm)76-43225-7676-17825-51
Discharge Setting (mm)22-38.16.4-15.86.4-15-193.2
Power (kW)300-50025-30300-50025-30


Typical Metso Cone Crusher Capacities

CrusherTypeFeed Opening (mm)Lmin (mm)Capacity (tph)
HP800 Standard HeadFine26725495-730
HP800 Short HeadFine335---
MP1000 Standard 2392 mmFine30025915-1210


Commercial Cone Crushers

Principle Technical Data of Cone Crusher Series
Principle Technical Data of Cone Crusher Series

Cone Crushers Product Distributions

Cone Crusher Stone Grade Distribution
Cone Crusher Stone Grade Distribution

Gyradisk Cone Crusher

  • For finer size products (e.g., -6 mm), a special cone crusher known as the Gyradisc is commonly used.
  • Operation is similar to the Standard Cone Head; however, breakage is mostly by attrition rather than impact.
  • Reduction ratio is around 8:1.
  • Feed size is limited to less than 50 mm with a nip angle between 25° and 30°.
  • Head diameters are between 900 and 2100 mm.
  • The Gyradisc is normally maintained in choke feed mode.
  • Product size between 6 and 9 mm.


GyraSphere System Diagram
Gyrasphere System Diagram [image: (135-5-22)]

Impact Crushers

  • One or two heavy rotors carrying fastened projections, revolve inside a cas1ng.
  • The projections break the rock by primary impact and propels the rock against the case for the secondary impact.
  • Impactors are utilized in soft and non- abrasive applications.


Impact Crusher Diagram
Impact Crusher Diagram [image: (135-5-23)]


  • Can handle a large size reduction: 1 m to 75mm
  • High reduction ration for amount of investment.
  • Impactor provides a high degree of fines (for ores).
  • Can handle up to 2500 MTPH.


  • Power consumption is higher as more fines are produced.
  • Cannot handle tramp metal.
  • Requires feeder.

Gyradisc Cone Crusher












































AMIT 135: Lesson 4 Performance Modeling & Assessment


Upon completing this lesson students should be able to:

  • Explain the method used to assess the performance of separators.
  • Illustrate partition analysis for comminution circuit.
  • Analyze different types of partition curves.
  • Explain the methods to access separation efficiency from partition curve.

Reading & Lecture

Partition Analysis

  • One of the most insightful methods for quantifying the performance of separators is a “partition analysis”.
  • This detailed assessment is commonly performed using a “partition curve”.
  • Partition curves show the probability of a particular particle having a given characteristics reporting to a given product stream.
  • Can be achieved for any separation: particle size, density, magnetics, floatability, etc.
Density tracers recovered form floats and sinks immediately show the partition curve.
Density tracers recovered from floats and sinks immediately show the partition curve. [image: (135-4-1)]


  • To explain partition curves, let’s take a look at a “perfect” particle size separation at 0.45 mm.
  • As shown, 100% of particles > 0.45 mm in each in each size class in the feed report to oversize.
A diagram depicting perfect particle separation
A diagram depicting perfect particle separation
[image: (135-4-2)]


  • If the separation is less than perfect, then particles can be “misplaced” to the wrong streams.
  • This includes:
    • Misplacement of coarser particles to undersize
    • Misplacement of finer particles to oversize
A diagram illustrating less then perfect particle separation
Less then perfect particle separation
[image: (135-4-3)]

A diagram comparing two separation curves
A Comparison of separation curves
[image: (135-4-4)]
  • If ideal, curve runs parallel to abscissa at the “cutsize”.
  • More deviation from axis means more misplaced material.
  • Shape is characteristic of separator type and operation.

  • Cut – Point
    = D50
    = 0.45 mm
  • Ecart Probability (Ep)
    = [D75-D25]/2
    =(0.5-0.4)/2=0.05 mmImperfection (I)
    =0.05/2 = 0.025
Partition probability curve
Partition probability curve

  • Curve shape is an inherent characteristic of the type of separator employed.
  • Commonly reported values for imperfection range from 0.005 to more than 0.50.
  • Depends on:
    • Type of equipment (e.g., screens, cyclones hydraulic sizers, etc)
    • Characteristics of feed material (e.g., particle size, shape, density, etc.)
    • Production demands (feed rate, water quality, etc.)
A diagram comparing separation efficiency
A comparison of separation efficiency
[image: (135-4-6)]

  • Another important issue is “bypass”.
  • Bypass can occur to both oversize and undersize.
  • Oversize bypass is not unusual for screens
  • Undersize bypass very common for classifiers.
A diagram depicting bypass results
A diagram depicting bypass results
[image: 135-4-7)]

  • Bypass is the misplacement of fines via entrainment  into the oversize  product.
  • Quantified by zero-size offset on the partition curve.
  • Can sometimes >30°/o  for fine sizing applications.
  • Bypass typically has a large adverse downstream impact.
  • Classifiers are often used in multiple stages  to  reduce bypass  (i.e., retreat oversize).
Bypass diagram
[image 135-4-8]

Acceptable Curves:

  • Type 1- Ideal Symmetrical
    • represents perfect  processes (e.g., laboratory sieve  data)
  • Type 2 – Efficient Symmetrical
    • OK for  efficient units (e.g., well  designed/operated  screen)
  • Type 3 – Inefficient Symmetrical
    • OK for less efficient units (e.g., fine hydraulic classifiers)
Acceptable separation curves
Acceptable separation curves
[image: (135-4-9)]

Undesirable Curves:

  • Type 4- Oversize Nonsymmetrical
    • shows loss of coarse to undersize (e.g., holes in screens)
  • Type 5 – Undersize Nonsymmetrical
    • shows loss of fines to oversize (e.g., overloaded screen)
Undesirable separation curves
Undesirable separation curves
[image: (135-4-10)]

Inherent unit characteristic, poor circuit design, excessive rates, mechanical failure, poor operating practices, others …

Step 1- Collect Samples

  • Collect representative samples of the feed, oversize and undersize streams.
  • Make sure that all streams have been taken into account.

Step 2 – Perform Size Analysis

  • Perform a laboratory particle size analysis on each sample.
  • Assess data to make sure that it is reliable (discussed later).

Ball mills

Size Class (Mesh)Mean Size (mm)Feed Mass (%)U/S (%)O/S (%)

Step 3 – Conduct Calculations

  • Plot (u-f) versus (u-o).
    Data should form a line passing  through  zero .
  • Line slope is the fraction of feed tonnage that reports to oversize.
  • You may disregard unreliable points that do not appear to fall along the line.
Size Class (Mesh)Mean Size (mm)Feed Mass (%)U/S (%)O/S (%)X-axis (u-o)Y-axis (u-f)
A graph showing line slope partition
Observations? Slope in the first plot shows that 46% of feed reported to oversize.
[image: (135-4-11)]

Step 4 – Construct Partition Curve

  • Calculate oversize partition for each size class using [(u-f)o]/[(u­ o)f].
  • Plot mean size versus partition factor .
  • Compute performance indicators (cutsize, imperfection, bypass, etc.).


Mean Size (mm)Feed Mass (%)U/S (%)O/S (%)Y-axis (u-f)X-axis (u-o)Percent Feed Weight
Percent Feed Weight
Reconstituted Feed WeightPartition Number

Yield to Oversize Stream – 46.92%


Slope in first plot shows that 46 .9% of feed reported to oversize. Partition curve shows 0.30 mm cutsize, no oversize bypass and 9% undersize bypass. [image: (135-4-12)]

Partition Curve Observations

  • The partition curve completed for a particle size separation utilized the weight distribution of all process streams including the feed stream.
  • Depending on the  breakage characteristics of the material and the  location of the sample points, particle breakage could occur  which  affects the component balance around the process.
  • As such, it is sometimes preferred to use component assays (e.g., solid concentration or assays such as iron content) and the two-product equation to determine mass yield.
  • Using the mass yield, the feed  is then  reconstituted to determine  the  partition  numbers.

Corrected Partition Number

The equation for determining the corrected Partition Number is:

Y' = \frac{Y-R_{1}}{1-R_{1}-R_{2}} (5-10)

Y’ is the corrected partition number, Y the actual partition number, R1 , the fractional amount of ultrafines by-passing to the underflow stream and R2 , the fractional amount of coarsest particles by-passing to the flow stream.

  • The by-pass of coarse material to the overflow stream is rare but may occur due to a worn vortex finder.
  • R2 =0 can be assumed in most cases.

A chart showing a mean particle size curve.

Separation Efficiency

Separation efficiency should always be measured from the corrected partition numbers.

  •  Bypassed particles were not subjected to the separation forces .

For particle size separations, the imperfection value (I) is the preferred measurement:

I = \frac{d_{75} - d_{25}}{2d_{50}}

d75, d50 , and d25= the particle size having 75 %, 50% and 25% probabilities, respectively,  of reporting to the underflow stream.

Probability of Underflow
Percent Probability of Underflow
[image: (135-4-14)]

Separation Performance Projection

  • Many equations are available that model typical performance curves associated with
  • Lynch and Rao found that the Reduces Efficiency curve can be modeled by the following expression:

Y' - \frac{exp(\alpha \chi )-1)}{exp(\alpha \chi ) + exp(\alpha )-2))} \; \; \; \; (5-11)

X= d/d 50(c)

α = the curve slope and the value is indicative of the classification efficiency.

  • The Lynch model can be used to predict the performance of a classifying cyclones.
Chart showing increasing values of alpha
[image: (135-4-15)] Chart showing increasing values of alpha

Example: Performance Prediction

Given a feed particle size distribution and an alpha value of 2.5, predict the performance of a cyclone. The amount of ultrafine by-pass is assumed to be 20% by weight.

Mean Particle Size (microns)Weight (%)d/d50(c)Corrected Partition NumberActual Partition NumberUnderflow Weight (%)Normalized Underflow Weight (%

Mass Yield to Underflow = 61.57%


  • “Partition factor” represents the probability that a given particle size in the feed stream will report to the oversize  product.
  • “Partition analysis” makes it possible to determine key performance indicators.
    • Cutsize (D50)
    • Imperfection (I)
      • Bypass
  • Plant personnel should monitor and strive to maintain sizing “efficiencies ” since this greatly impacts other plant operations.

















AMIT 135: Lesson 3 Particle Size Distribution


After completing this lesson students should be able to:

  • Demonstrate understanding of various method involved in measuring particle size.
  • Explain the importance of particle size analysis and its application.
  • Differentiate between the different models used for predicting particle size.
  • Explain the different convention followed in measuring particle size.

Reading & Lecture

Mineral Particle Sizes

  • Particles within a given process stream vary in size and shape.
  • Quantifying the amount of material within a given size fraction is often important for design and operational considerations.
  • Particles that are either spherical or cubical are relatively easy to characterize.
  • However, the majority of particles are often neither of these two shape types.
  • Particle size characterization can be determined by:
    • Microscopic Analysis
    • Sieving
    • Sedimentation (Stokes Diameter)
    • Optical (Laser deflection or reflection)

Mean Particle Sizes

  • The mean particle size of a distribution is typically measured by either the arithmetic or geometric mean of the maximum (dmax) and minimum (dmin) particle sizes.
  • The arithmetic mean is most accurate for symmetric particles such as spheres or cubes.
    d{am} = \frac{d{max} + d{min}}{2}
  • The geometric mean is typically preferred when segregation of the particles into various fraction were achieved by passing particles through an opening having a given shape and area, e.g., screening.
    d{gm} = (dmax * dmin)^{\frac{1}{2}}) = (d{1}d{2}d{3}...d{n})^{\frac{1}{N}}N = number of particles or size fractions

Particle Size Analysis

Sieve Opening Size (mm)Mean Particle Size (mm)Weight (#)Cumul. % RetainedCumul. % Finer
Nest of Sieves
Diagram of a nest of sieves.
  • The top size was estimated to be the square root of two times the top sieve size or 1.4mm.
  • There is 5% retained on the 1mm screen.
  • If the total feed was directed to the 0.3mm screen, 40% of the feed would be retained on the screen.
  • 95% of the feed is finer than 1mm and 20% is finer than 0.15mm.
  • The mean size of the material passing the 0.15mm screen can be estimated assuming the bottom size is 1 micron.


Particle Sizes Distribution Models

  • There is a common need to determine the amount of material in the feed at a given particle size.
  • The desired particle size may not have been included in the original particle size analysis.
  • The two common models used include:
  1. Gates-Gaudin-Schuhmann Model (GGS)
  2. Rosin-Rammler Model (RR)
  • The RR model is typically satisfactory for coarse distributions.
  • The GGS model is generally considered more precise for fine particle size distributions.
  • It may be needed to perform model fits over more than 2 particle size rangers.


Gates-Gaudin-Schumann Model

A chart showing particle size chart from the Gates-Gaudin-Schumann Model
[image: (135-3-1)]
The GGS model predicts the cumulative percent passing distribution:

Y = 100(\tfrac{x}{k})^{m}

Y= cumulative percent passing

x= particle size

k= size parameter

m =distribution parameter

The values of k and m can be determined by linear regression:

log y = m log x + k

Rosin-Rammler Model (RR)

A particle size chart showing the Rosin-Rammler Model (RR)
[image: (135-3-2)]
  • The Rosin-Rammler model is typically used to predict the % retained.
  • The modified equation to predict the % finer is:Y = 100 - 100exp \left [ -\left ( \frac{x}{R} \right )^{b} \right ]

R= size parameter

b= distribution parameter

  • There is special graph paper available to help determine the correct values of R and b over any size range.


Volume Mean Diameter

The mean particle size by volume is important when dealing with topics such as material transport, storage and hindered particle settling velocities.

The volume mean diameter, d_{3}^{v} , can be quantified by:

d_v = \left (\frac{\sum_{i=1}{M_i}}{\sum_{i=1}\frac{M_i}{d^3}} \right )^\frac{1}{3} = \left ( \frac{1}{\sum_{i=1}\frac{M_i}{d^3}} \right )^\frac{1}{3}

Where M_{i} is the mass within size fraction i.

Mean Size Fraction Diameter (mm)dp3Mass, Mi (%)Mi/d3

d_v = \left ( \frac{100}{11315.83} \right )^\frac{1}{3} = 0.206mm



Surface Mean Diameter

  • The surface mean diameter is important when considering surface coatings with chemicals, particle agglomeration and dewatering.
  • The volume mean diameter, ds , can be quantified by:d_{s} = \left ( \frac{particle mass per diameter}{particle mass per volume} \right )^{\frac{1}{2}} = \left ( \frac{\Sigma_{i-1} \frac{M_{i}}{d_{i}}}{\Sigma_{i-1} \frac{M_{i}}{d^{3}}} \right )^{\frac{1}{2}}
    where Mi is the mass within the size fraction i.
Mean Size Fraction Diameter (mm) \dpi{200} d_{3}^{p} Mass, Mi (%) \dpi{200} \frac{M_{i}}{d_{3}^{i}} \dpi{200} \frac{M_i}{d_i}
0.8 0.512 10 20 13
0.6 0.216 40 185 67
0.3 0.027 30 1111 100
0.125 0.002 20 10000 160
Total 100 11315 340

d_{s} = \left ( \frac{340}{11316} \right )^{\frac{1}{2}} = 0.173






AMIT 135: Lesson 2 Circuit Mass Balancing


Introductory narrative or video


Upon completion of this lesson students should be able to:

  • Differentiate between different type metallurgical accounting methods and benefit of metallurgical accounting.
  • Recall the definitions of grade, recovery, yield and other characteristics used in mass balancing.
  • Recognize the application of two product formula for balancing.
  • Provide a brief idea about multi component balancing for complex ores.


Mass and Volume Balancing

Mass and Volume Balancing
Outotec Concentrator
The most important rule governing the accounting of a processing plant or unit operation is that mass can be neither created nor destroyed.

Mass In = Mass Out

Volume In = Volume Out

Mass and Component Balance

Mass Component Balance
Outotec Concentrator
The component balance is true for any assay type such as any element content, % finer than, water-to-solids ratio etc.

Ff = Cc + Rr

Mass Yield or Mass Recovery

Mass Yield or Mass Recovery
Outotec Concentrator

\LARGE \mathbf{Mass\; Yield, Y = \frac{tons/hr\; Plant\; Concentrate}{tons/hr\; Plant\; Feed} = \frac{C}{F}}

Two-Product Formula

Given the mass and component balance equations :

F = C + R

Ff = Cc + Rr

Mass yield (Y) can be solved as a function of the stream, assays which yields the two-product  formula:

R = F- C

Ff = Cc + r (F – C)

Mass Yield, Y = \frac{C}{F} = \frac{(f-r)}{c-r}



Mass Yield Formula Example

Mass Yield, Y = \frac{C}{F} = \frac{(f-r)}{c-r}

Mass Yield = \frac{(0.50 - 0.14)}{(24.5 - 0.14)}\ast 100

Mass Yield = 1.5%

Mass Yield Formula Diagram

Component Recovery

In many mineral processing applications, the focus is to maintain maximum recovery of the valued mineral or element while also maximizing upgrade or concentrate assay.

Component Recovery = \frac{Cc}{Ff} = \frac{c}{f} \ast \frac{(f-r)}{c-r} = \frac{c}{f}\ast Y

Mass Yield or Mass Recovery
Outotec Concentrator


Component Recovery Example

Cu Recovery, R = Y\ast \frac{c}{f}

Cu Recovery, R = 1.5\ast \frac{(24.5)}{(0.50)}\ast 100

Cu Recovery, R = 73.5%



Concentration Ratio, CR

Concentration Ratio, CR = \frac{c}{f}

Mass Yield Formula Diagram



Complex Sulfide Ore Metallurgical Balance

Brunswick No.1 Concentrator

Process Stream Weight (%) Assays
Pb% Zn% Cu% Ag%
Mill Feed 100.00 3.21 7.93 0.33 2.26
Copper Concentrate 0.74 4.69 4.65 22.64 50.39
Lead Concentrate 4.80 42.20 9.62 0.33 15.48
Zinc Concentrate 10.52 1.12 57.76 0.18 1.75
Tailings 83.94 1.22 1.61 0.15 1.14
Metal Recovery (%) 63.1 76.6 50.9



Section Process Stream Mass Flow (tph) Copper Assay (%) Cu Recovery (%)
Complete Plant Mill Feed 709 0.53 100
Mill Concentrate 10 33.00 88.3
Mill Tailings 699 0.06 11.7
Rougher Feed 716 0.55
Concentrate 28 12.00 83.6
Tailings 688 0.09
Scavenger Feed 253 0.13
Concentrate 6 2.00 2.4
Tailings 247 0.09
Cleaner Feed 29 12.00
Concentrate 15 22.00
Tailings 14 1.30
Re-Cleaner Feed 18 20.00
Concentrate 11 31.00
Tailings 7 3.00
Final Cleaner Feed 11 31.00
Concentrate 10 33.00 88.3
Tailings 1 5.00

Mass/Volume Flow Determination

  • The relationship between the mass (M) and the volume flow (Q rates in a given stream is defined as:M=\frac{Q\rho_{p} X}{100}
    \rho_{p} = the pulp density (solids and water) in lbs/ft3
    X = solids concentration in % by weight
  • Volumetric flow rate can be measured by flow meters, P-Q curve relationships for pumps or directly measured.
  • Pulp density can be measured using a Marcy Density of nuclear density gauge.
  • The solids concentration can be estimated using a common expression or directly measured.

Pulp Density

  • Density (&rho;) is the ratio of the mass weight (M) of a substance and the total volume (V):
    \rho = \frac{Mass}{Volume} = \frac{M}{V}
  • Water has a density of:
    • 1.0gm/ml or 1.0gm/cm3
    • 1000kg/m3 – 1tonne/m3
    • 62.4lbs/ft3
  • Specific gravity is the ratio of the material density over the density of water:\frac{\rho }{\rho _{w}} = \frac{\rho }{62.4lb/ft^{3}}

Marcy Scale

  • The Marcy scale is a common tool used in preparation plants to measure pulp density.
  • The scale uses a container that allows a volume of exactly 1000 ml.
  •  After collecting  the sample,  the container  is hung on a weight  scale which measures in grams.
  • The printed scale reads the pulp density directly in grams/ 1ml.
  • Since water density is 1.0 gm/ml, the scale also indicates the specific gravity of the pulp.\frac{\rho _{p}}{1.0gm/ml}
Marcy Scale
A Marcy scale



Mass Flow Determination Example

A classifying cyclone is being fed slurry at a volumetric flow rate of 1000 gpm. The specific gravity of the slurry is 1.1 and the solids concentration was determined to be 15.0°/o by weight. Determine the mass feed flow rate in tons per hour:

M=\frac{Q\rho _{p}X}{100}

M=\frac{(Q gal/min)(0.13368ft^{3}/gal)(^{3})(X)(60min/hr)}{(2000lbs/ton)(100)}

M=\frac{(Q\rho _{p}X)(}{(4)(100)}


M (tph) = \frac{(100 gal/min)(1.1)(15.0)}{(4)(100)}=41.3 tph

Volumetric Balancing Using Pulp Density

  • Pulp density measurements around unit operations such as dense medium separators and classifying, cyclones can be used to assess volume yield.
  • Consider the balance around a classifying cyclone:Q_{f}=Q_{u}+Q_{o}
    Q_{f}\rho _{f}=Q_{u}\rho _{u}+Q_{o}\rho _{o}
    since (Qvol/time)\ast (\rho\: mass/volume)= Pulp\: mass/time
  • Thus, the volumetric yield to the underflow stream can be obtained from the following expression:Volume\: Yield\: to\: Underflow=\frac{Q_{u}}{Q_{f}}=\frac{(\rho _{f}-\rho _{o})}{(\rho_{u}-\rho _{o})}\times 100
A diagram depicting formulas for figuring the balance around a classifying cyclone
Formulas for figuring the balance around a classifying cyclone
[diagram 135-2-1]

Slurry Solids Concentration by Weight

A classifying cyclone is treating 150 gallons/min of slurry. A plant technician has measured the pulp densities of the process streams using a Marcy density gauge and reported the following: ρf = 1.08 gm/ml, ρo =  1.03 gm/ml and ρu = 1.20 gm/ml. Determine the volumetric flow rates to each stream.


Y_{u}=\frac{(\rho_{f}-\rho _{o})}{(\rho _{u}-\rho _{o})}\times 100=  _________%

Q_{u}=Q_{f}Y_{u}=150 \times  _________ = _________ gallons/min

Q_{o}=150- _________ = 150 X (1 – _________) = __________ gallons/min

  • The solids concentration X of a slurry by weight can be measured directly by:
    • Collecting a sample,
    • Measuring the weight of the total slurry or pulp Mp
    • Drying the sample and
    • Measuring the dry weight of solids Ms

      X=\frac{M_{s}}{M_{p}}\times100= \frac{M_{s}}{M_{s}+M_{w}}\times 100Mw = water weight
  • This equation is often used to determine the amount of water in a process stream1 knowing the solids concentration by weight and the tons/hr of solids in a process stream.


Solids Concentration Example

The underflow stream from the classifying cyclone bank contains 100 tons/hour of ore which represents 45% of the total slurry mass.

The downstream concentrators require a feed solids concentration of 30% by weight. How much water is required to be added to dilute the stream to the required solids concentration?


Water in Cyclone Underflow = M_{w}=\frac{100tph}{0.45} - tph=  ________ tph

Water\: in\: Spiral\: Feed = M_{w} = \frac{100 tph}{0.30} - 100 tph =  ________ tph

Dilution\: Water\: Required = Q = \frac{(400)(m)}{(} = \frac{(400)(\; \; \; \; \; \; \; )}{(1)(100)} =  ________ tph

= _______ gpm


% Solids & Pulp Density Relationship

  • It often occurs that the knowledge of the solids content is needed within a time frame less than the sample preparation and analysis time.
  • When this situation arises, the solids content by weight can be estimated knowing the pulp density (ρp =) as measured with the Marcy scale and using the following equation:
    X% = \frac{\rho _{s}(\rho _{p}-\rho _{w})}{\rho _{p}(\rho _{s}-\rho _{w})}\times 100ρs = solids density or specific gravity
    ≈ 2.65 for most host rock minerals.ρw = water density (62.4 lbs/ft3 or 1gm/ml) or specific gravity (=1).

Estimation of Solid Density

  • The density of  solid can be estimated if you know the composition by weight or volume of each component in the solid and the respective solid densities.
  • For example, assume that raw ore is a two component system comprised of a valued mineral and host rock having relative densities of 6.30 and 2.65, respectively. The amount of valued mineral is 30% of the total ore.Total Solid Mass, M: Mineral + Host Rock – 30 + 70 = 100
    Total Volume, Vs:  {\color{Red} \frac{M_{M}}{\rho_{M}}+\frac{M_{HR}}{\rho _{HR}} = \frac{30}{6.30}+\frac{70}{2.65}= 31.18}

    Total Solid Relative Density {\color{Red} =\frac{M_{s}}{V_{s}} - \frac{100}{31.18} = 3.21}


Circuit Balancing

  • The data generated from process units and circuits are used to make important decisions.
    • Plant design considerations
    • Operational  efficiencies
    • Potential upgrades
  • As such, reliable data is very important for an operating plant.
  • All data must be checked for proper balancing based on the ‘laws of conservation’.
  • ‘What goes in’ = ‘What goes out’


Material Balancing

Balance Summary
Overall:  F = C+R

Pb: Ff1 = Cc1 + Rr1
Zn: Ff2 = Cc2 + Rr2
L/S Ratio: Ff3 = Cc3 + Rr3


  • Is this a good set of data?
  • Which values are not reliable?
A diagram of a material balance equation
[image 135-2-2]

Material Balance

Overall Balance

F = C+R

100 = 90 + 10

100 = 100

Image of a thumbs up

A diagram of a material balance equation
[image 135-2-3]

Lead Balance

Ff = Cc+ Rr

100(5.20) = 90(0.20) + 10 (50.20)

520.00=18.00 + 502.00

520.00= 520.00

Image of a thumbs up

A diagram of a material balance equation
[image 135-2-4]

Zinc Balance

Ff = Cc+ Rr

100(2.30) = 90(0.30) + 10 (22.30)

230.00= 27.00+223.00

230.00 ≠250.00

Image of thumbs down

A diagram of a material balance equation
[image 135-2-5]

Slurry Balance

Mass balance equations must be satisfied!

  • Must use 1/Solids%
Product StreamMass (tph)Solids (%)Inverse SolidsSlurry (tph)

Water Balance

L/S Ratio Balance

Ff = Cc+ Rr

100(3.0) = 90(4.0) + 10(1.0)

300= 360+10

300 ≠370

Example: 3.0 = 3 parts Water to 1 part Solids = 25%

Image of thumbs down

A diagram of a material balance equation
[image 135-2-6]

Two-Product Formula


F = C + R

Ff = Cc + Rr


Multiply by r:

Ff = Cc + Rr

-(Ff = Cc + Rr)


Ff- Ff = Cr – Cc


F (r-f) = C (c-r)




Yield = C/F = (r-f) / (r-c)


* Only assays needed to get product-to- feed ratio

Two-Product Formula (Pb assays)


C/F = 10/100

= 10%




= 10%

A diagram of a material balance equation
[image 135-2-7]

Two-Product Formula Characteristics

  • Formula only applies under steady-state conditions
  • Formula very sensitive to variations in the reject assay, “r”
  • Formula inaccurate when component is not separated
  • Formula may calculate different yields for each assay (due to experimental errors)

Two-Product Formula (various assays)


C/F = (5.2-0.2)/ (50.2-0.2)

= 10%




= 9%



C/F = (1/25-1/20) / ( 1/50-1/20)

= 33%

A diagram of a material balance equation
[image 135-2-8]

What to Do with Unbalanced Data

Eliminate  Data

  • avoid collecting or ignore data that conflicts
  • most common approach in industry
  • arbitrary and highly subject to user biases
  • not getting full value out of your data

Adjust  Data

  • create consistent balances by adjusting data
  • use method of “weighted least squares”
  • adjustments should (i) satisfy all mass balances equations and (ii) be as small as possible





AMIT 135: Lesson 1 Introduction


Insert intro narrative or video.


By the end of this lesson students should be able to:

  • Explain the role of Extractive Metallurgy and its sub disciplines in mining industry.
  • Explain mineral processing and processes involved.
  • Distinguish between ore, mineral and rocks.
  • List different physical properties of ore and how they are exploited in beneficiation process.
  • Develop an understanding how beneficiation process works based on a typical example flowsheet of various ore.


The economical production of metals and non-metals has never been as important and as difficult as it is today. In the twentieth century, annual copper production increased by a factor of 250 to an amount exceeding 8 million tons per year. A greater increase was realized by aluminum with similar trends also observed for other metals such as lead, zinc and tin. Occurring simultaneously with the increase in demand of most metals, industrial minerals and fuels, the quality of the ore reserves have depreciated substantially.

Iron ore on a conveyor
Iron Ore on a conveyor [image 135-1-1]
Digging ore from the earth is only half the battle. Often just as challenging and costly is the processing of the ore, which takes place in mills, smelters and refineries. Processing requires crushing and grinding to liberate the minerals. After liberation, separation processes are used to concentrate the valuable mineral. The final step removes water from the concentrate and tailings.


Copper ore
Copper ore, image courtesy of Aibyek Khamkhash
[image (135-1-2.1]
Photograph of pyrite stacked cubes, from the National Mineral Collection
Photograph of pyrite stacked cubes (R18657) from the National Mineral Collection
Uranium ore
Uranium ore
[image 135-1-2.3]
[image 135-1-2.4]

Today’s ore reserves are lower in grade and the minerals are more finely disseminated, thereby making minerals processing of the material more complex and costly. Finely disseminated ores require substantial comminution costs to liberate the valuable minerals. In 1986, it was estimated that 35% of selling price for copper was associated with the crushing and grinding of host ore.

A copper mine
A copper mine, image courtesy of Aibyek Khamkhash
[image 135-1-3]

Extractive Metallurgy

The study of the processes used in the separation and concentration (benefication) of raw materials. The field is an applied science, covering all aspects of the physical and chemical processes, used to produce mineral-containing and metallic materials, sometimes for direct use as a finished product, but more often in a form that requires further physical processing which is generally the subject of physical metallurgy, ceramics, and other disciplines within the broad field of materials science.


  • Minerals Processing
  • Hydrometallurgy
  • Pyrometallurgy
  • Electrometallurgy

Mineral Processing

The science and art of converting a run-of-mine ore into a saleable and/or usable product by means that do not destroy the physical and chemical identity of the minerals.

Distinct objectives include:

  • Production of a saleable material having a specified particle size distribution (e.g. aggregate industry).
  • Liberation of components for subsequent processing (e.g. exposing surfaces for leaching processes).
  • Generation of a material having a specified composition, e.g.,
    • Elimination of components that would hinder the efficiency of downstream processes.
    • Elimination of components that would limit the feasibility of using the materials as a saleable product.
  • Objective ‘c’ involving the production of a final concentrate tends to be the most complex and difficult forms of mineral processing since it involves several distinctly different operations, i.e.,
    • Liberation (crushing and grinding);
    • Particle Size Control (screening and classification);
    • Composition Control (solid-solid separations);
    • Product and Tailings Dewatering (solid-liquid separations).


A diagram of mineral processing
A diagram of mineral processing [image 135-1-4]


The term “aggregate” is defined as gravel, sand, clay, shale, stone, limestone, sandstone, marble, granite, “rock”.

In the definition of aggregate the term “rock” excludes metallic ores and the non-metallic ores: barite, coal, diamond, graphite, gypsum, kaolin, magnesite, mica, salt and talc.

The production of aggregates is relatively simple. The process typically involves a series of crushers and screens to produce material having various particle sizes.

Importance of Aggregates

  • Aggregates touch our lives everyday, from the driveway to the workplace. We drive, sit, stand and walk on aggregates.
  • Many products that enrich our daily lives contain aggregates. They are found in paint, paper, plastics and glass. In powder form, aggregates are used as mineral
    supplements for agriculture, medicines and household products.
  • Aggregates are also used to protect the environment by controlling soil erosion, assisting in water purification and reducing sulfur dioxide emissions generated by power plants.

Aggregate Production

At the beginning of the 20th century, production of aggregates in the United States was minimal and its uses limited. Today, aggregates are produced in every state, and aggregates production tonnage ranks first in the non-fuel minerals industry.

More than two billion tons of aggregates are used annually in the United States. This equals ten tons of aggregates for every American!

Aggregate pile
Aggregate pile
[image 135-1-5]
An aerial view of the Barrick Gold mine
Barrick Gold mine
[image 132-1-5.2]

Aggregate Preparation Circuits

  • Grizzly Screens: Removes fines to bypass primary crushers.
  • Crushers: Reduces the size of material.
  • Screens: Separation aggregates into various sizes.
A screen with rock
A screen
[image 135-1-6]

A typical mill flowsheet diagram
A Typical Flow Sheet diagram [image 135-1-7]

Iron Ore Processing

The mineral types are:

  • Hemattite (Fe2O3)
  • Magnetite (Fe3O4)

Typical gangue material is silica

In some cases, the iron ore deposit is sufficiently rich and thus no physical processing is required.

Where processing is required, separation processes typically include:

  • Density-based separators
  • Magnetic separators
  • Froth flotation
An iron ore processing plant
An iron ore processing plant
[image 135-1-9]

Iron Processing Circuits

  • Grinding (9”- powder-fine)
    • Primary Mill Grinding
    • Pebble Mill Grindin1g
  • Concentrating:
    • Deslime thickeners
    • Magnetic separator
    • Vacuum disc filters
  • Producing Pellets:
    • Balling: The powdery iron ore concentrate is mixed with a small amount of a clay binder called “bentonite” and rolled into marble-sized  pellets.
    • Rotary Kiln: Heat-hardening of pellets at temperatures as high as 2,400 °F.
Iron ore Processing diagram
Iron ore Processing diagram
[image 135-1-10]

Iron ore pellets
Iron ore pellets [image 135-1-12]

Iron ore processing flowsheet
Iron ore processing flowsheet
[image 135-1-13]

Gold and Silver Processing

  • Grinding and Size Classification.
  • Leaching and Adsorption:
    • Addition of water to form slurry .
    • Addition of lime to the ore and cyanide solution to the slurry, to leach the gold or silver.
    •  Addition of carbon to adsorb dissolved metals.
  • Recovery and Dore Bullion
    • Stripping the metals from the carbon by acid washing .
    • Precipitation of the gold and silver by electro-wining.
    • Smelting of metal products into bars of dore bullion.
    • Pumping of the barren slurry (tailings) to the tailings storage facility.
[image 135-1-14.1]
Gold minerals
Gold minerals [image 135-1-14.2]
Gold ore processing flowsheet
Gold ore processing
[image 135-1-15]

Nickel Processing

  • Size Reduction: Primary, secondary and tertiary crushers.
  • Magnetic Separation: Separates magnetic ore (pyrrhotite) from non-magnetic ore (copper and nickel concentrates).
  • Froth Flotation: Non-magnetic ore is sent to a series of rougher and cleaner flotation cells to produce nickel concentrate.
  • Drying: Thermal  removal of liquid moisture .
  • Calcining: Thermal decomposition of a material.

Nickel Processing Circuits

  • Roasting: Thermal gas-solid reactions, which can include oxidation, reduction, chlorination, sulfation, and pyrohydrolysis.
  • Smelting: Thermal reactions in which at least one product is a molten phase.
  • Refining: Removal of impurities from materials by a thermal process .
Nickel Ore
Nickel ore
[image 135-1-18.1]
Nickel processing flowsheet
Nickel processing flowsheet
[image 135-1-18.2]

Diamond Processing

  • Crushing
  • Screening
  • Heavy-Medium Separation (HMS)
  • X-ray Sorter
Aerial photo of the Ekati diamond mine
Ekati diamond mine
[Image 135-1-19.1]
A rough diamond
A rough diamond [image 135-1-19.2]
A 70 carat white rough diamond
Rough diamond from the Diavik Diamond Mine, 70 carat
[image 135-1-19.3]
A cut diamond
A cut diamond
[image 135-1-19.4]
Diamond processing flowsheet
Diamond processing flowsheet [image 135-1-20]


Uranium Processing

  • Crushing and Grinding Circuit: Particle size reduction for leaching efficiency.
  • Thickener: Removal of excess water from ground ore.
  • Leaching: Acid is used to dissolve uranium from the ore.
  • Washing and Filtering: Separation of uranium solution from solid waste.
  • Solvent Extraction and Strip Section: Removal of uranium from water ­kerosene solution to aqueous solution.
  • Precipitation Tanks: Uranium precipitates (yellowcake) upon addition of ammonia.
  • Thickener: Excess water is removed.
  • Centrifuge: Moisture removal.
  • Calciner: Removal of ammonia and production of uranium oxide (U3O8).
Uranium yellow cake
Uranium Cake
[Image 135-1-21]

Uranium ore processing flowsheet
Uranium ore processing flowsheet
[Image 135-1-22]

Platinum Processing


  • Size reduction: Crushing and milling circuits
  • Rougher and Cleaner Flotation: Separation of platinum from ore
  • Tailings and Concentrate Thickening: Removal of excess water.
  • Filtering: Removal of moisture.
[Image 135-1-23]

Platinum Processing Circuits


  • Drying: Thermal removal of water
  • Smelting : Thermal reactions in which at least one product is a molten phase



  • Base Metals Refinery: Nickel, copper and cobalt
  • Platinum Metals Refinery: Platinum, Rhodium, Iridium, Ruthenium, Palladium and gold
Platinum processing flowsheet
Platinum processing flowsheet
[image 135-1-24]

Zinc Processing Circuit

  • Size reduction: Crushing and grinding.
  • Flotation: Zinc is separated from the ore.
  • Filtering: Removal of excess water and surface.
[image 135-1-25]
Zinc metal
Zinc Metal
[image 135-1-25.2]
[image 135-1-25.3]
Zinc flowsheet
Zinc flowsheet
[image 135-1-26]

Zinc and lead processing flowsheet
Zinc and lead processing flowsheet
[image 135-1-27]

Heavy Mineral Sand

  • Main products of heavy mineral sands processing are:
    • Rutile (TiO2)
    • Ilmenite (FeTiO3)
    • Leucoxene
    • Zircon (ZrSiO4)
  • Titanium Dioxides
    • Paints
    • Plastics
    • Paper
    • Textiles
    • Inks
    • Foodstuffs, cosmetics
[image 135-1-28.1]
[image 135-1-28.2]


  • Zircon is generally a minor product obtained from processing heavy mineral sands.
  • Applications
    • Ceramics in opacifiers used in surface glazes and pigments.
    • High melting  point (2200°C) attracts use as a foundry sand in moulds
    • Zirconium metal
      • 90% in nuclear energy
    • Zirconium Metal
    • Zirconium chemicals
Zirconium Metal
Zirconium Metal
[image 135-1-29]
Zirconium silicate powder
Zirconium silicate powder
[image 135-1-29]

Heavy Mineral Sand Properties

Mineral Valuable Magnetic Susceptibility Electrical Conductivity SG Chemical Formula
Ilmenite Yes High High 4.5-5.0 FeTiO3
Rutile Yes Low High 4.2-4.3 TiO2
Zircon Yes Low Low 4.7 ZrSiO4
Leucoxene Yes Semi High 3.5-4.1 Fe.TiO3.TiO2
Monazite No Semi Low 4.9-5.3 (Ce,La,Th,Nd,Y)PO4
Staurolite No Semi Low 3.6-3.8 Fe2Al9Si4O22.(OH)
Kyanite No Low Low 3.6-3.7 Al2SiO5
Garnet No Semi Low 3.4-4.2 (Fe,MN,Ca)3.Al2(SiO4)3
Quartz No Low Low 2.7 SiO2


Magnetic & Non-Magnetic Density Fractionation

Magnetic Non-Magnetic
SG Mineral SG Mineral
-3.85 Trash -3.79 Quartz, trash
-3.85 + 4.05 Magnetic Leucoxene -3.79 + 4.05 Leocoxene
-4.05 + 4.38 Altered Ilmenite -4.05 + 4.38 Rutile
-4.38 + 4.9 Primary Ilmenite -4.38 + 4.9 Zircon
+4.9 Monazite +4.9
Image of a floating dredge and concentrator
Dredge and floating concentrator (3000-4000tph) [image 135-1-30]
[image of dredge and floating concentrator (3000-4000tph)
Dredge and floating concentrator (3000-4000tph) [image 135-1-31]
A diagram of a spiral concentrator
A spiral concentrator [135-1-32]
A diagram of spiral concentrators
spiral concentrators [135-1-33]
General Heavy Mineral Sand Concentration Process diagram
General Heavy Mineral Sand Concentration Process [image (135-1-34)]

Wet High Intensity Magnets (WHIMS)

After the initial gravity concentration, WHIMS can be used to separate ilmenite from the other heavy minerals.

A diagram of a wet high-intensity magnet
WHIMS [image 135-1-35]
Typical Dry Processing Process Flow Sheet of Heavy Mineral Sands
Typical Dry Processing Process Flow Sheet of Heavy Mineral Sands
[image 136-1-36]

High Tension Electrostatic Separators
High Tension Electrostatic Separators [image (135-1-38)]



















AMIT F135: Syllabus


Title: Introduction to Mining Systems and Equipment

Department/Number: AMIT 135

Credits: 4

Prerequisites: N/A

Location: Fairbanks Pipeline Training Center (FPTC) Room #2

Meeting Dates/Time: TBD


Name: Tathagata Ghosh, Aibyek Khamkhash

Office Location: 317 Duckering Building, University of Alaska Fairbanks

Office Hours: by Appointment

Telephone/Email: 907-474-6917


Course Textbook: Wills’ Mineral Processing Technology, 8th edition

B.A Wills, James Finch PhD, Butterworth-Heinemann publisher, 2015

ISBN-13: 978-0080970530



Supplementary Readings: as provided

Any Supplies Required: Notebook or 3 ring binder to store handouts


An overview to the field of mining beneficiation and comminution, systems and equipment used for the mining and mineral processing industry. Fundamentals of basic separation and mineral beneficiation, economic planning, environmental concerns, safety and terminology will be explored.


The goal of the student is to gain broad knowledge of the equipment and processes used in large scale mine mill operations. The student will learn about separation and comminution equipment used, and the control and analysis operators use to control quality.


Upon completion of this course the student will be able to:

  1. Identify the role of a mill operator technician in the control of separation and comminution in the mill.
  2. Understand and explain the terminology used to describe the equipment and systems in mill operations.
  3. Understand and explain mine mill process drawings.
  4. Students demonstrate an understanding of safety as applied to working in a mill facility
  5. Students demonstrate proper safety practices around rotating equipment
  6. Students demonstrate knowledge of various types of crushing equipment.
  7. Students demonstrate knowledge of various types of grinding equipment circuits.
  8. Students demonstrate knowledge of mineral processing fundamentals.


Instructional methods will include lectures, reading assignments, homework, labs, the use of the Blackboard system, and other digital media.


Assignments and due dates will be provided in class or through the blackboard system.


Students are expected to comply with the University Student Code of Conduct available for review at:


Classroom Ground Rules:

  1. Turn off cell phones during class. If you must maintain cell phone contact, put the ringer on vibrate and leave the class room to receive a call.
  2. No laptop computers are allowed during class without instructor’s permission.
  3. If you are late for class by over 15 minutes you will receive .5 attendance point. Please find a vacant seat and be seated with a minimum of disturbance to the class.
  4. Respect instructor and classmates.
  5. Restrict talking or conversations that do not include the entire class or add value to the class discussion.
  6. If you do not understand a concept, idea, or explanation, you should ask the instructor or classmate to explain it in a different manner.
  7. All tests will be administered in a closed book- no notes format.

Homework, Class Notes, Power Point presentations, notebooks and Blackboard:

Students are expected to submit legible homework written in a manner suitable for the assignment. Shorthand answers will not be accepted. Answers must communicate the content of the question. The process of writing out both the question and the answer helps the student to retain the information. As an employee you will be expected to communicate clearly in your written communications and this class expects the same level of communication.

As a student you are responsible for taking notes and making certain you understand the information presented. A notebook is a good way to capture and retain this information. Information not covered in your assigned reading will be made available in lecture, in a digital format, or in hard copy. All Class assignments will be initiated from Blackboard. (You may be directed away from Blackboard but you will start in the Blackboard Assignments folder.)

Class Attendance and Participation:

Class attendance and participation is very important for meeting the course objectives. Attendance will be taken at the start of each class. Students who are working a rotating shift schedule or missing class on a regular basis need to make prior arrangements with the instructor. The student’s participation portion of the grade is based on the quality (not frequency) of your participation. Those receiving high grades in class participation are those who:

  1. Have prepared for class by completing reading assignments prior to the lecture.
  2. Understand and have completed all assignments neatly, accurately and on-time.
  3. Participate in class discussions by sharing experiences or asking/answering questions.
  4. Present Safety Huddle discussions.
  5. Are willing to volunteer for in-class demonstrations and exercises.
  6. Class participation will be an earned grade for each scheduled class. If you are late you will lose .5 point for class participation. If you are absent you lose the entire point.
  7. Unexcused absences will lose one attendance point. Excused absences will lose .5 attendance point. Excused means that you notified the instructor before the beginning of class. (As you would do if you were notifying an employer.)

Make Up work Policy

Homework and assignments turned in later than the test covering the assignment will receive zero credit and may not be evaluated. Keeping up with class work is expected. If you cannot be present for a test you should contact the instructor beforehand and schedule a time to make up the test. Tests not scheduled for make-up within a week will be scored as a 0.


Grading Scale                                               Evaluation System

A = 100-90%                                                  Exams                                     30%

B =   89-80%                                                  Homework                              20%

C =   79-70%                                                  Attendance/Participation     20%

D =   69-60%                                                  Final Exam                              30%

F =   59% or less

* Plus and minus grades will not be submitted

* The Final exam is comprehensive and will be drawn from material covered over the entire semester.


Extensive support services are available for the student and can be found on the web at: Students are encouraged to form study groups with their peers. The instructor is available to assist students on an as scheduled basis. Students are encouraged to take full advantages of all these services.


UAF has a Disability Services office that operates in conjunction with the College of Rural and Community Development’s (CRCD) campuses and UAF’s Center for Distance Education (CDE). Disability Services, a part of UAF’s Center for Health and Counseling, provides academic accommodations to enrolled students who are identified as being eligible for these services.If you believe you are eligible, please visit on the web or contact a student affairs staff person at your nearest local campus. You can also contact Disability Services on the Fairbanks Campus at (907) 474-7043,

UAF Title IX

University of Alaska Board of Regents have clearly stated in BOR Policy that discrimination, harassment and violence will not be tolerated on any campus of the University of Alaska. If you believe you are experiencing discrimination or any form of harassment including sexual harassment/misconduct/assault, you are encouraged to report that behavior. If you disclose sexual harassment or sexual violence to a faculty member or any university employee, they must notify the UAF Title IX Coordinator about the basic facts of the incident.

Your choices for disclosure include:

1) You may confidentially disclose and access confidential counseling by contacting the UAF Health & Counseling Center at 474-7043;

2) You may access support and file a Title IX report by contacting the UAF Title IX Coordinator at 474-6600;

3) You may file a criminal complaint by contacting the University Police Department at 474-7721