“Optimum Design and Analysis of Swinging Jaw Plate

of a Single Toggle Jaw Crusher”

Thesis Submitted in Partial Fulfillment of the Requirements for the Award of

Master of Technology In

Machine Design and Analysis

By

B B V L Deepak Roll No: 208ME103

Department of Mechanical Engineering National Institute of Technology

Rourkela 2010

“Optimum Design and Analysis of Swinging Jaw Plate of a Single Toggle Jaw Crusher”

Thesis Submitted in Partial Fulfillment of the Requirements for the Award of

Master of Technology In

Machine Design and Analysis

By

B B V L Deepak Roll No: 208ME103

Under the Guidance of

Dr. N. KAVI

Department of Mechanical Engineering

National Institute of Technology Rourkela

2010

ACKNOWLEDGEMENT

Successful completion of work will never be one man’s task. It requires hard work in right

direction. There are many who have helped to make my experience as a student a rewarding one.

In particular, I express my gratitude and deep regards to my thesis guide Prof. N. Kavi

first for his valuable guidance, constant encouragement and kind co-operation throughout period

of work which has been instrumental in the success of thesis.

I also express my sincere gratitude to Prof. R. K. Sahoo, Head of the Department,

Mechanical Engineering, for providing valuable departmental facilities.

Last but not the least; I wish to express my sincere thanks to all those who directly or

indirectly helped me at various stages of this work.

B B V L Deepak

National Institute Of Technology

This is to certify that the thesis entitled,

Jaw Plate of a Single Toggle Jaw Crusher

fulfillment of the requirements for the award of Master of Technology Degree in

Engineering with specialization in

Technology, Rourkela is an authentic work carried out by him under my supervision

guidance.

To the best of my knowledge, the matter embodied in the thesis has not been submitted to

any other University / Institute for the award of any Degree or Diploma.

Date:

National Institute Of Technology

Rourkela

CERTIFICATE

This is to certify that the thesis entitled, “Optimum Design and Analysis of Swinging

Jaw Plate of a Single Toggle Jaw Crusher” submitted by Mr. B B V L Deepak

of the requirements for the award of Master of Technology Degree in

with specialization in “Machine Design and Analysis” at the National Institute of

Technology, Rourkela is an authentic work carried out by him under my supervision

To the best of my knowledge, the matter embodied in the thesis has not been submitted to

any other University / Institute for the award of any Degree or Diploma.

Dr. N. Kavi

Department of Mechanical Engineering

National Institute of Technology

Rourkela

Design and Analysis of Swinging

B B V L Deepak in partial

of the requirements for the award of Master of Technology Degree in Mechanical

at the National Institute of

Technology, Rourkela is an authentic work carried out by him under my supervision and

To the best of my knowledge, the matter embodied in the thesis has not been submitted to

Dr. N. Kavi

Department of Mechanical Engineering

Institute of Technology

Rourkela-769008

CONTENTS

Title Page No.

Abstract i

Nomenclature ii-iii

List of figures iv-vi

List of tables vii

Chapter 1 Introduction and Scope for Study

1.1 Introduction 1

1.2 Overview of Jaw Crushers 2

1.2.1 Introduction to Jaw Crusher 2

1.2.2 Different Types of Jaw Crusher 3

1.3 Major Components of a Jaw Crusher 5

1.4 Jaw Crusher working principle 8

1.5 Crusher Sizes and Power Ratings 10

1.6 Different Performance Parameters of Jaw Crusher 10

1.7 Objective of Present Work 11

Chapter 2 Literature Review 12

Chapter 3 Theoretical Analysis and Data Collection

3.1 Introduction to Kinematics of Machines 18

3.1.1 Study of Machines 18

3.1.2 Kinematics of Machines 18

3.1.3 Classification of Mechanisms 19

3.1.4 Four-Bar Linkage 20

3.2 Jaw Crusher as a Crank- Rocker Mechanism 21

3.3 Choosing the Points along the Liner for Computing 22

3.4 Movement Computation and Feature Analysis of Points 24

3.5 Squeezing Process & Particle Breakage 31

3.5.1 Fractured Size Distribution 31

3.5.2 Squeezing Process 32

3.6 Introduction to Design of Jaw Plates 34

3.6.1 The load distribution along the swing plate 36

3.6.2 Modeling irregular particle behavior with that of cylinders 37

3.7 Experimental Data Collection 38

3.7.1 Point load deformation and failure (PDF) data for materials 38

3.7.2 Effects of size on both strength and deformability 39

3.8 Design Swing Jaw Plates 42

3.9 Finite Element Analysis 43

3.9.1 Introduction to Finite Element Method 43

3.9.2 Finite Element Analysis Applications 43

3.9.3 Modeling using Four-Node "Tetrahedral" Element 44

Chapter 4 Computational Study for Swinging Jaw Plate and Swinging Lever

4.1 An introduction to Computer Aided Design (CAD) 49

4.1.1 An Introduction to CATIA 50

4.1.2 Solid Modeling of Swing Jaw Plate and Pitman using CATIA 51

4.2 Computer Aided Analysis 53

4.2.1 Generative Structural Analysis in CatiaV5 53

4.3 Finite Element Analysis 53

4.3.1 Pre-Processing 53

4.3.2 Computation 54

4.3.3 Post-Processing 54

4.3.4 Mesh Refinement Iteration 54

4.3.5 Report Generation 54

4.4 Static Stress Analysis of Assembled Structure Using CATIA 54

4.4.1 Assumptions 54

4.4.2 Applying Material 55

4.4.3 Assembling of Swinging Jaw Plate and Pitman 55

4.4.4 Fastened connections 56

4.5 Linear Static Stress Analysis 57

4.5.1 Applying Boundary Conditions 57

4.5.2 Analysis for Optimizing the Toggle Plate Width 58

4.5.3 Anlysis for Optmizing the Toggle Plate Location 62

4.5.4 Analysis by considering stiffeners to the swinging jaw plate 66

4.6 Validation of results 68

Chapter 5 Results, Discussion and Conclusion

5.1 Force Distribution along the Swinging Jaw Plate 69

5.2 Wear Analysis 70

5.3 Optimization of Width and Location of Toggle Plate 71

5.4 Optimization of Mass of the Swinging Jaw Plate 71

5.5 Conclusion 74

References 75

i

ABSTRACT

A jaw crusher is a kind of size reduction machine which is widely used in mineral,

aggregates and metallurgy fields. The performance of jaw crusher is mainly determined by the

kinematic features of the swing jaw during the crushing process. The practical kinematic

characteristic of the points located along the swing jaw plate are computed and discussed. Based

on the analysis of the liner movement and the crushing parameters, force distribution along the

swing jaw plate is obtained. The job is helpful for a design of new prototype of this kind of

machine on optimizing the frame, designing the chamber and recognizing the crushing character.

The interaction between jaw plates and material particles brings the inevitable and serious

wear to the jaw plates during the jaw crusher operation, which not only decreases the efficiency,

but also increases the cost and the energy consumption of the jaw crusher. Obtained results from

the kinematic analysis of the moving jaw and the crushing force distribution analysis, the jaw

plates wear is analyzed on a macroscopic level. It is helpful to design the crusher for improved

performance.

Efforts to decrease energy consumed in crushing have lead to consideration of decreasing

the weight of the swing plate of jaw crushers. Design of lighter weight jaw crusher will require a

more precise accounting of the stress and deflections in the crushing plates than is available with

traditional technique. The design of swing jaw plate is carried out by using CAD i.e., jaw plate

has been solid modeled by using CATIAV5R16. FEA is applied to assembled structure of

swinging jaw plate and lever to optimize the width and location of the toggle plate along the

swinging lever. The different comparisons of swing jaw plates behavior, calculated with the

traditional and the new FEA failure models with stiffeners, shows that 24% savings in plate

weight may be possible.

Keywords: Jaw Crusher, Kinematic Features, Liner, Force Distribution, Wear Analysis, Finite Element Analysis, Computer Aided Design (CAD), Stiffened Jaw Plate.

ii

Nomenclature

l Length of coupler

r eccentric or crank length

k Toggle plate length

x Horizontal displacement

y Vertical displacement

vx Velocity in X direction

vy Velocity in Y direction

vu Velocity in U direction

vv Velocity in V direction

ax Acceleration in X direction

ay Acceleration in Y direction

au Acceleration in U direction

av Acceleration in V direction

Ф Crank angle made by vertical

Ө Nipping angle

ω Angular velocity of eccentric shact

µ Co-efficient of friction

f frictional force

N Normal force

Q Total Loading Force

T Toggle Force

q� Unconfined Compressive Strength

iii

P Maximum Point Load

S� Tensile Strength

X Proportionality Factor

d Diameter of Specimen

D Diametral Deformation

R Radius of Rock Particles

ν Poisson’s Ratio

�� Young’s Modulus of Rock

K and a Power law Deformation Descriptors

�� Load at failure

� Deformation at failure

�� Normalized failure loads

� Normalized Deformation at failure

M Mass of the swinging jaw plate

iv

List of Figures

Fig 1.1.Typical Jaw Crusher 3

Fig.1.2. Types of Blake Type Jaw Crusher 4

Fig.1.3. Dodge Type Jaw Crusher 5

Fig.1.4. Sectional view showing Components of a Jaw Crusher 7

Fig.1.5. Working Principle of Jaw Crusher 9

Fig.3.1 Types of four-bar linkages 21

Fig.3.2 Jaw Crusher sketch 22

Fig.3.3 Points track along the liner 23

Fig.3. Point consideration in dynamic coordinate 24

Fig.3.5 Horizontal Displacements 25

Fig.3.6 Vertical displacements 25

Fig.3.7 6th Point Track 26

Fig.3.8 6th Point horizontal Displacement 26

Fig.3.9 6th Point vertical Displacement 26

Fig.3.10 Horizontal velocities 26

Fig.3.11. Vertical velocities 27

Fig.3.12 U-directional Velocities 28

Fig.3.13 V-directional Velocities 28

Fig.3.14 Horizontal accelerations 29

Fig.3.15 Vertical accelerations 29

Fig.3.16 U-directional accelerations 30

Fig.3.17 V-directional accelerations 30

v

Fig.3.18 Fracture caused by compression crushing 31

Fig.3.19 Particle fracture mechanism 31

Fig.3.20 Forces on particle during crushing 32

Fig.3.21 Elevation View of Jaw Crusher 34

Fig.3.22 Idealization of particles within jaw crusher 35

Fig.3.23 Modeling of particles within jaw crusher 35

Fig.3.24 Load distribution along plate 36

Fig.3.25 Comparison of plate and point-loaded particles. 37

Fig.3.26 Comparison of the effect of size on point load at failure 39

Fig.3.27 Effect of specimen size on ultimate strength and deformability 41

Fig.3.28 Overall Dimensions of Typical Jaw Crusher 42

Fig.3.29 Tetrahedron Element in Global xyz- System 45

Fig.4.1 Swinging jaw plate without stiffeners 52

Fig.4.2 Swinging jaw plate with one stiffener 52

Fig.4.3 swinging jaw plate with two stiffeners 52

Fig.4.4 swinging jaw plate with three stiffeners 52

Fig.4.5 swinging lever or pitman of the single toggle jaw crusher 52

Fig.4.6 assembled structure of swinging jaw plate with pitman 52

Fig.4.7 Finite Element Analysis Process in CATIA 54

Fig.4.8 Assembly constraints applied to jaw plate and pitman 55

Fig.4.9 Property on the constraint 57

Fig.4.10 Boundary conditions to the pitman 57

Fig.4.11 Toggle Plate of the jaw crusher 58

Fig.4.12 Vonmisses stresses vs toggle plate width 59

Fig.4.13 displacements vs toggle plate width 59

vi

Fig.4.14 Von Misses Stress and Displacements for the Toggle plate width of 100mm 59

Fig.4.15 Von Misses Stress and Displacement for the Toggle plate width of 200mm 60

Fig.4.16 Von Misses Stress and Displacement for the Toggle plate width of 400mm 60

Fig.4.17 Von Misses Stress and Displacement for the Toggle plate width of 600mm 61

Fig.4.18 Von Misses Stress and Displacement for the Toggle plate width of 800mm 61

Fig.4.19 Von Misses Stress and Displacement for the Toggle plate width of 900mm 62

Fig.4.20 Von Misses stress vs toggle location 62

Fig.4.21 displacement vs toggle location 62

Fig.4.22 Von Misses Stress and Displacement ,Toggle plate located at bottom 63

Fig.4.23 Von Misses Stress and Displacement ,Toggle plate at 50mm from bottom 63

Fig.4.24 Von Misses Stress and Displacement ,Toggle plate at 100mm from bottom 64

Fig.4.25 Von Misses Stress and Displacement ,Toggle plate at 150mm from bottom 64

Fig.4.26 Von Misses Stress and Displacement ,Toggle plate at 200mm from bottom 65

Fig.4.27 Von Misses Stress and Displacement ,Toggle plate at 250mm from bottom 65

Fig.4.28 swinging jaw plate with one stiffener, two stiffeners, three stiffeners 66

Fig.4.29 Von Misses Stress and Displacement ,using single stiffener 67

Fig.4.30 Von Misses Stress and Displacement ,using two stiffeners 67

Fig.4.31 Von Misses Stress and Displacement ,using two stiffeners 67

Fig.5.1 Force distribution considering X and Y direction accelerations 69

Fig.5.2 Force distribution considering U and V direction accelerations 70

Fig.5.3 Mass of one stiffener jaw plate 71

Fig.5.4 Mass of two stiffeners jaw plate 72

Fig.5.5 Mass of three stiffeners jaw plate 72

vii

List of Tables

Table 1.1 Jaw Crusher Performances 10

Table 3.1: PE400*600 Jaw Crusher Calculation Parameters 21

Table 3.2: variation of nip angle with crank angle 24

Table 3.3 Materials tested 38

Table 3.4 Summary or point-load strengths and deformability 40

Table 3.5 Effect of size on average point-load strength and deformability 41

Table 3.6 Dimensional chart for Jaw Crusher 42

Table.4.1 Material properties of swinging jaw plate & pitman 55

Table.4.2 Von Misses stress and displacements at various sizes of the Toggle Plate widths 58

Table.4.3 Von Misses stress and displacement, swinging jaw plate with stiffeners 66

Table.4.4 Comparison of results with Chrlesh H. Dowding results 68

Table.5.1 Von Misses stress, Deformation and Mass of the jaw plate with stiffeners 73

CHAPTER-1

INTRODUCTION AND SCOPE FOR STUDY

1

1. INTRODUCTION AND SCOPE FOR STUDY

1.1 Introduction

The first stage of size reduction of hard and large lumps of run-of-mine (ROM) ore is to

crush and reduce their size. Large scale crushing operations are generally performed by

mechanically operated equipment like jaw crushers, gyratory crusher and roll crushers. The

mechanism of crushing is either by applying impact force, pressure or a combination of both.

The jaw crusher is primarily a compression crusher while the others operate primarily by the

application of impact.

The breakage mechanism of the jaw crusher is rather simple. The crushing process is

composed of serials of single particle breakage. After a particle is nipped in the chamber and

failed in tension stress, the resulting fragments drop down to new position before being nipped

and squeezed. When particles meet the size demand, they leave the chamber from the outlet. It is

obvious that the movement of the moving jaw is a key factor to jaw crusher performance. An

accumulation of the jaw plates wear will change the crushing chamber geometry. At the same

time, the geometry variation of moving jaw results in the movement change, which has great

effect on the nipping action and the particle fracture.

Based on the analysis of the moving jaw movement, the squeezing process and the

crushing force distribution, the jaw plates wear on a macroscopic level is studied aiming to

effectively predict the wear distribution on the jaw plates.

Many engineering structures consist of stiffened thin plate elements to improve the

strength/weight ratio. The stiffened plates subjected to impact or shock loads are of considerable

importance to mechanical and structural engineers.

The main objective of the present work is to describe the movement of the moving jaw in

detail and analyze the breakage squeezing process. Obtained results from the analysis of the

moving jaw movement, the squeezing process, the crushing force distribution and the jaw plates

wear on a macroscopic level is studied aiming to effectively predict the wear distribution on the

jaw plates. And propose an efficient use of modeling in the connection between the plate and the

stiffener has been described.

2

1.2 Overview of Jaw Crushers

1.2.1 Introduction to Jaw Crusher

The first stage of size reduction of hard and large lumps of run-of-mine (ROM) ore is to

crush and reduce their size. Softer ores, like placer deposits of tin, gold, mineral sands etc. do not

require such treatment. Large scale crushing operations are generally performed by mechanically

operated equipment like jaw crushers, gyratory crusher and roll crushers. For very large ore

pieces that are too big for receiving hoppers of mechanically driven crushers, percussion rock

breakers or similar tools are used to break them down to size. The mechanism of crushing is

either by applying impact force, pressure or a combination of both. The jaw crusher is primarily

a compression crusher while the others operate primarily by the application of impact. [6]

Jaw crusher is one of the main types of primary crushers in a mine or ore processing plant.

The size of a jaw crusher is designated by the rectangular or square opening at the top of the jaws

(feed opening). For instance, a 24 x 36 jaw crusher has a opening of 24" by 36", a 56 x 56 jaw

crusher has a opening of 56" square. Primary jaw crushers are typically of the square opening

design, and secondary jaw crushers are of the rectangular opening design. However, there are

many exceptions to this general rule. Jaw crusher is a primary type of crusher which has two

jaws, out of which one is stationary attached rigidly with the crusher frame whereas the other

moves between a small throw forward and retarded back successively to crush the ore or rock

boulders.

Jaw crushers are typically used as primary crushers, or the first step in the process of

reducing rock. They typically crush using compression. The rock is dropped between two rigid

pieces of metal, one of which then move inwards towards the rock, and the rock is crushed

because it has a lower breaking point than the opposing metal piece.

Jaw crusher movement is obtained by using a pivot point located at one end of the “swing jaw”,

and an eccentric motion located at the opposite end. [6]

3

Fig 1.1.Typical Jaw Crusher [36]

1.2.2 Different Types of Jaw Crusher

Jaw crusher can be divided into two according to the amplitude of motion of the moving

face. The different types of Jaw Crushers are:

1) Blake Type Jaw Crusher

In this the movable jaw is hinged at the top of the crusher frame so that the maximum

amplitude is obtained at the bottom of the crushing jaws. Blake Crushers are operated by toggles

and controlled by a pitman. These are commonly used as primary crushers in the mineral

industry. The size of the feed opening is referred to as the gape. The opening at the discharge end

of the jaws is referred to as the set. The Blake crushers are single or double toggle drives. The

function of the toggle(s) is to move the pivoted jaw. The retrieving action of the jaw from its

furthest end of travel is by springs for small crushers or by a pitman for larger crushers. As the

reciprocating action removes the moving jaw away from the fixed jaw the broken rock particles

slip down, but are again caught at the next movement of the swinging jaw and crushed. This

process is repeated until the particle sizes are smaller than the smallest opening between the

crusher plates at the bottom of the crusher (the closed set). For a smooth reciprocating action of

the moving jaws, heavy flywheels are used in both types of crushers. Blake type jaw crusher may

be divided into two types. [6]

4

(a) Single toggle type: - In this the number of toggle plate is only one. It is cheaper and has less

weight compare to a double toggle type jaw crusher. The function of the toggle(s) is to move the

pivoted jaw.

(b) Double toggle type: - Here the number of toggle plate is two. Over the years many mines

have used the double-toggle style of crusher because of its ability to crush materials; including

mineral bearing ores those were both tough and abrasive. While many aggregate producers have

used the overhead eccentric style. There are many factors that should be considered when

deciding which style would be best for your application. For larger material crushing, always

larger Blake type jaw crushers are selected. The characteristics of this type of crusher are as

following

1. Larger, rough, blocky as well as sticky rock or ore lumps can be crushed.

2. Reinforcement of the crusher is possible with the help of high strength crusher frame to crush

very hard rock or ore lumps.

3. It is very simple to adjust to prevent much of wear and also very easy to repair,

4. Maintenance o the crusher is very easy.

Single-Toggle Jaw Crusher Double-Toggle Jaw Crusher

Fig.1.2. Types of Blake Type Jaw Crusher [43]

5

2) Dodge Type Jaw Crusher The moving plate is pivoted at the bottom and connected to an eccentric shaft. In universal

crushers the plates are pivoted in the middle so that both the top and the bottom ends can move.

The movable jaw is hinged at the bottom of the crusher frame so that the maximum amplitude of

motion is obtained at the top of the crushing jaws. They are comparatively lower in capacity than

the Blake crushers and are more commonly used in laboratories.

Fig.1.3. Dodge Type Jaw Crusher [6]

1.3 Major Components of a Jaw Crusher

Crusher Frame:

Crusher Frame is made of high welding. As a welding structure, it has been designed with

every care so as to ensure that it is capable of resistant to bending stress even when crushing

materials of extremely hard.

Jaw Stock:

Jaw Stock is also completely welded and has renewable bushes, Particular importance has

been given to jaw Stock of a design resistant to bending stresses. All jaw stocks are provided

with a renewable steel Alloy or manganese steel toggle grooves.

Jaw Crusher Pitman:

The pitman is the main moving part in a jaw crusher. It forms the moving side of the jaw,

while the stationary or fixed jaw forms the other. It achieves its movement through the eccentric

machining of the flywheel shaft. This gives tremendous force to each stroke.

6

Thus it appears this is just the name that was applied to this part. Pitman is made of high quality

steel plates and carefully stress relived after welding. The Pitman is fitted with two renewable

steel Alloy or manganese steel toggle grooves housings for the bearings are accurately bored and

faced to gauge.

Manganese Dies in the Jaw Crusher:

The jaw crusher pitman is covered on the inward facing side with dies made of manganese,

an extremely hard metal. These dies often have scalloped faces. The dies are usually

symmetrical top to bottom and can be flipped over that way. This is handy as most wear occurs

at the bottom (closed side) of the jaw and flipping them over provides another equal period of

use before they must be replaced.

Jaw Crusher Fixed Jaw Face:

The fixed jaw face is opposite the pitman face and is statically mounted. It is also covered

with a manganese jaw die. Manganese liners which protect the frame from wear; these include

the main jaw plates covering the frame opposite the moving jaw, the moving jaw, and the cheek

plates which line the sides of the main frame within the crushing chamber.

Eccentric Jaw Crusher Input Shaft:

The pitman is put in motion by the oscillation of an eccentric lobe on a shaft that goes

through the pitman's entire length. This movement might total only 1 1/2" but produces

substantial force to crush material. This force is also put on the shaft itself so they are

constructed with large dimensions and of hardened steel. The main shaft that rotates and has a

large flywheel mounted on each end. Its eccentric shape moves the moving jaw in and out.

Eccentric Shaft is machined out of Alloy Steel Fitted with anti-friction bearings and is housed in

pitman and dust proof housing.

Jaw Crusher Input Sheave/Flywheel:

Rotational energy is fed into the jaw crusher eccentric shaft by means of a sheave pulley

which usually has multiple V-belt grooves. In addition to turning the pitman eccentric shaft it

usually has substantial mass to help maintain rotational inertia as the jaw crushes material.

7

Fig.1.4. Sectional view showing Components of a Jaw Crusher

Toggle Plate Protecting the Jaw Crusher:

The bottom of the pitman is supported by a reflex-curved piece of metal called the toggle

plate. It serves the purpose of allowing the bottom of the pitman to move up and down with the

motion of the eccentric shaft as well as serve as a safety mechanism for the entire jaw. Should a

piece of non-crushable material such as a steel loader tooth (sometimes called "tramp iron") enter

the jaw and be larger than the closed side setting it can't be crushed nor pass through the jaw. In

this case, the toggle plate will crush and prevent further damage.

Tension Rod Retaining Toggle Plate:

Without the tension rod & spring the bottom of the pitman would just flop around as it isn't

connected to the toggle plate, rather just resting against it in the toggle seat. The tension rod

system tensions the pitman to the toggle plate. The toggle plate provides a safety mechanism in

case material goes into the crushing chamber that cannot be crusher. It is designed to fail before

8

the jaw frame or shaft is damaged. The seats are the fixed points where the toggle plate contacts

the moving jaw and the main frame.

Jaw Crusher Sides Cheek Plates:

The sides of the jaw crusher are logically called cheeks and they are also covered with

high-strength manganese steel plates for durability.

Jaw Crusher Eccentric Shaft Bearings:

There are typically four bearings on the eccentric shaft: two on each side of the jaw frame

supporting the shaft and two at each end of the pitman. These bearings are typically roller in

style and usually have labyrinth seals and some are lubricated with an oil bath system. Bearings

that support the main shaft. Normally they are spherical tapered roller bearings on an overhead

eccentric jaw crusher.

Anti-Friction Bearings are heavy duty double row self-aligned roller-bearings mounted in

the frame and pitman are properly protected against the ingress of dust and any foreign matter by

carefully machined labyrinth seals. Crushing Jaws are castings of austenitic manganese steel

conforming to IS 276 grade I & II. The crushing jaws are reversible to ensure uniform wear and

tear of grooves.

Jaw Crusher Adjustment: Closed Side Opening Shims

Depending on the disposition of the material being crushed by the jaw different maximum

sized pieces of material may be required. This is achieved by adjusting the opening at the

bottom of the jaw, commonly referred to as the "closed side setting". Shims (sometimes

implemented and a more adjustable or hydraulic fashion) allow for this adjustment. [41]

1.4 Jaw Crusher Working Principle

The working principal of Jaw Crusher is based on modern design "CRUCHING WITHOUT

RUBBING" The machine consists, two Jaws, one fixed and the other moving. The opening

between them is smaller at the bottom and wider at the top. The pitman moving on an eccentric

shaft on bearing, swing lever (Moving Jaw) swing on center pin. The Rock held in between two

Jaws and crushed by mechanical pressure.

Fig.1.5. Working Principle of Jaw Crusher

The motor drives the belt pulley and the belt pulley drives the eccentric shaft to rotate, and

make the moving jaw approach and leave the fixed jaw periodically

shaft rotation, to crush, rub and grind the materials

and slower and gradually fall down and finally discharge from the discharge opening

desired dimension of the crushed product

stationary breaking surface whi

the stationary plate.

The ore or rock is fed to the crusher where the jaws are furtherest apart, i.e. at the

maximum opening or gape. When the jaws come together the ore is crushed

and slip down in the crushing chamber

experienced and the ore moves down further. The process is repeated till particles having size

less than the bottom opening or set pass through as

move the pivoted jaw. The retrieving action of the jaw from its furthest end of travel is by

springs for small crushers or by a pitman for larger crushers. For a smooth reciprocating action

of the moving jaws, heavy flywheels are used in both types of crushers

the eccentric shaft.

9

Fig.1.5. Working Principle of Jaw Crusher [42]

The motor drives the belt pulley and the belt pulley drives the eccentric shaft to rotate, and

approach and leave the fixed jaw periodically with respect to eccentric

, to crush, rub and grind the materials repeatedly, thus to make the material slower

and slower and gradually fall down and finally discharge from the discharge opening

desired dimension of the crushed product. A fixed jaw mounted in a “V” alignment is the

stationary breaking surface while the movable jaw exerts force on the rock by forcing it against

The ore or rock is fed to the crusher where the jaws are furtherest apart, i.e. at the

opening or gape. When the jaws come together the ore is crushed

crushing chamber. In the return stroke, further reduction of size is

moves down further. The process is repeated till particles having size

opening or set pass through as product. The function of the toggle(s) is to

move the pivoted jaw. The retrieving action of the jaw from its furthest end of travel is by

springs for small crushers or by a pitman for larger crushers. For a smooth reciprocating action

heavy flywheels are used in both types of crushers mounted on each side of

The motor drives the belt pulley and the belt pulley drives the eccentric shaft to rotate, and

with respect to eccentric

repeatedly, thus to make the material slower

and slower and gradually fall down and finally discharge from the discharge opening as the

A fixed jaw mounted in a “V” alignment is the

le the movable jaw exerts force on the rock by forcing it against

The ore or rock is fed to the crusher where the jaws are furtherest apart, i.e. at the

opening or gape. When the jaws come together the ore is crushed into smaller sizes

. In the return stroke, further reduction of size is

moves down further. The process is repeated till particles having size

The function of the toggle(s) is to

move the pivoted jaw. The retrieving action of the jaw from its furthest end of travel is by

springs for small crushers or by a pitman for larger crushers. For a smooth reciprocating action

mounted on each side of

10

1.5 Crusher Sizes and Power Ratings

The size of a jaw crusher is usually described by the gape and the width, expressed as

gape x width. Performance of the jaw crusher is depends on the characteristics of ore, size of the

feed and the discharge openings, speed, throw, nip angle (angle between swinging jaw plate and

fixed jaw plate during operation) The common crusher types, sizes and their performance is

summarized in Table 1.1.Currently, the dimension of the largest Blake-type jaw crusher in use is

1600 mm x 2514 mm with motor ratings of 250-300 kW. The maximum diameter of the feed is

ranged in 80 to 85% of the width of the maximum opening. Such a heavy crusher (16540x

2150mm) crushes rock, mineral or ore varying from 22.5 cm to 30cm with a capacity ranging

from 420 to 630 ton per hour. The motor rpm and power are around 90 and 187.5 kW

respectively. The jaw and the sides of the unit are lined with replaceable wear resistant plate

liners. [6]

Table 1.1 Jaw Crusher Performances

Crusher Type

Size mm Reduction Ratio

Power, kW

Toggle Speed, rpm

Gape, mm

Width, mm

Range

Average

Min Max Min Max

Min Max Min Max Blake double toggle

125 1600 150 2100 4:1/9:1 7:1 2.25 225 100 300

Blake single toggle

125 1600 150 2100 4:1/9:1 7:1 2.25 400 120 300

Dodge Type

100 280 150 28 4:1/9:1 7:1 2.25 11 250 300

1.6 Different Performance Parameters of Jaw Crusher Crushing of ore, mineral or rock depends upon the characteristics of ore, size of the feed

and the discharge openings, speed, throw, nip angle (It is the angle between the jaw faces.

Generally it is around 20° to 23° in higher capacity jaw crusher), etc, of the crusher. The capacity

of the crushing depends upon the reduction ratio (It is the ratio between the size of the feed and

the size of the discharge. Higher the reduction ratio less the capacity of the crusher) nip angle

(increase in the angle will decrease of the capacity of crusher), increase in speeds, throw curved

shaped jaws, etc. will increase the capacity.

11

The Jaw Crusher should not be buried by the feeding minerals or ores which will tend to

chock the mouth of the crusher and open a power operated hook will be necessary to remove the

ore or mineral lumps which jam the crusher unit. Generally average reduction ratio is around 1.8

to 7 with a maximum setting of gap around 2 to 2.4mm. However this reduction ratio may vary

depending upon many operating condition. The jaws do not touch each other and have a wide

gap at the top. The faces that are flat or flat / convex (convex jaws are better which reduces the

frequencies of chocking and also increases the capacity of production).

1.7 Objective of Present Work

The objective of the present work is to improve the performance of a jaw crusher, is

mainly determined by the kinematic features of the liner to optimize the frame, design the

chamber and recognizing the crushing characters during the crushing process. Obtained results

from the analysis of the liner movement and the crushing parameters, the normal pressure on the

liner is adopted to describe the crushing force. The force distribution is analyzed with the

different operational parameters, so the force distribution along the liner is obtained. Based on

the analysis of the moving jaw movement, the squeezing process and the crushing force

distribution, the jaw plates wear on a macroscopic level is studied aiming to effectively predict

the wear distribution on the jaw plates.

The present work is to strive for a design and analysis of commercially available swing jaw

plates (including stiffening elements), that is 0.9 m (36 in.) wide with 304 mm and 51 mm (12

in. and 2 in.) top and bottom openings of jaw crusher. The finite element method is applied to the

analysis of the swing jaw plate assembled with swinging lever to optimize the width and location

of the toggle plate along the swinging lever. Also further study of swing jaw plate with stiffener

is done using finite element analysis. The design and modeling of swinging jaw plate is

accomplished by using CAD i.e. parametric design package (CATIAP3V5R15). By using this

package three dimensional model of pitman for single toggle jaw crusher has been developed.

Finite Element Analysis of jaw plates are carried out by using CATIAP3V5R159

(GENERATIVE STRCTURAL ANALYSIS) programming. This work is extended to improve

the strength/weight ratio of swing jaw plate by adding different number of stiffener elements on

the jaw plates.

CHAPTER -2

LITERATURE REVIEW

12

2. LITERATURE REVIEW

Jaw crushers are used to crush material such as ores, coals, stone and slag to particle

sizes. Jaw crushers operate slowly applying a large force to the material to be granulated.

Generally this is accomplished by pressing it between jaws or rollers that move or turn together

with proper alignment and directional force. The jaw crusher squeezes rock between two

surfaces, one of which opens and closes like a jaw. Rock enters the jaw crusher from the top.

Pieces of rock those are larger than the opening at the bottom of the jaw lodge between the two

metal plates of the jaw. The opening and closing action of the movable jaw against the fixed jaw

continues to reduce the size of lodged pieces of rock until the pieces are small enough to fall

through the opening at the bottom of the jaw. It has a very powerful motion. Reduction in size is

generally accomplished in several stages, as there are practical limitations on the ratio of size

reduction through a single stage.

The jaw crushers are used commercially to crush material at first in 1616 as cited by Anon

[1].It is used to simplify the complex engineering. Problem those were prevailing in Mining and

Construction sector. An important experimental contribution was made in1913; Taggart [2]

showed that if the hourly tonnage to be crushed divided by Square of the gape expressed in

inches yields a quotient less than 0.115 uses a jaw crusher.

Lindqvist M.and Evertsson C. M. [3] worked on the wear in rock of crushers which

causes great costs in the mining and aggregates industry. Change of the geometry of the crusher

liners is a major reason for these costs. Being able to predict the geometry of a worn crusher will

help designing the crusher liners for improved performance. Tests have been conducted to

determine the wear coefficient. The experiments have been carried out using quartzite, known

for being very abrasive. Crushing forces have been measured, and the motion of the crusher has

been tracked along with the wear on the crusher liners. The test results show that the wear

mechanisms are different for the fixed and moving liner. If there were no relative sliding distance

between rock and liner, would yield no wear. This is not true for rock crushing applications

where wear is observed even though there is no macroscopic sliding between the rock material

and the liners. The predicted worn geometry is similar to the real crusher. The objective of this

work, where wear was studied in a jaw crusher, is to implement a model to predict the geometry

of a worn jaw crusher.

DeDiemar R.B. [4] gives new ideas in primary jaw crusher design and manufacture of

Jaw crusher utilizing open feed throat concept, power savings and automation features. Jaw

13

crushers with two jaw openings can be considered to be a completely new design. Jaw crushers

are distinguished by reciprocating and complex movement of the moving jaw. Jaw crushers with

hydraulic drives produced in France and jaw crushers with complex movement of two-sided jaws

produced have advantages as well as a common shortcoming. This is due to the discharge gap

being almost vertical or sharply inclined so that a large part of the material is crushed only to a

size corresponding to the maximum width of the gap between the jaws at the crusher exit. A new

design has a gently sloping gap between the movable and stationary jaws .This causes material to

move slowly and be subjected to repeated crushing. In addition the movement of the movable

jaw relative to the stationary one is such that its stroke is equal both at the inlet and outlet of the

discharge gap when the eccentric moves in different quadrants. The power consumption of this

jaw crusher is low since the work of crushing is distributed between two quadrants. The

precrushed material falls under its own weight onto the movable jaws which are lowered by the

movement of the eccentric through the third and fourth quadrants. During this movement the

material moved down slightly along the gap between the jaws and comes in contact with the

movable jaws at approximately the time when they are furthest removed from stationary jaws.

The material is again crushed as the eccentric continues to move through the first and second

quadrant. The material thus undergoes repeated crushing when it passes through the gap between

the jaws. Efforts to intensify the crushing process and to increase throughput capacity of crushers

sometimes leads to interesting solutions of kinematic systems. Analysis of crusher operation

leads to the conclusion that development of their design is proceeding both along the path of

improved design and development of fundamentally new efficient kinematic systems.

Russell A.R., Wood D. M.[5] helps in failure criterion for brittle materials is applied to a

stress field analysis of a perfectly elastic sphere subjected to diametrically opposite normal

forces that are uniformly distributed across small areas on the sphere's surface. Expressions are

obtained for an intrinsic strength parameter of the material, as well as its unconfined compressive

strength. An expression for the unconfined tensile strength is obtained by introducing an

additional parameter accounting for the micro structural features of the material. The expressions

indicate that failure initiates in the sphere where the ratio between the stress invariant and the

first stress invariant is a maximum. Such a criterion does not coincide with the location of

maximum tensile stress. The expressions are used to reinterpret published point load test results

and predict unconfined compressive strengths. The configuration of the point load test as well as

surface roughness and elastic properties of the pointer and samples are taken into account to

14

establish the size of the area on which the point loads act. The predictions are in good agreement

with measured values obtained directly using unconfined compressive strength tests. It is

concluded that the point load test provides a more reliable estimate of the compressive strength

than the tensile strength.

Gupta Ashok and Yan D.S. [6] worked in design of jaw crushers which impart an impact

on a rock particle placed between a fixed and a moving plate. The faces of the plates are made of

hardened steel. Both plates could be flat or the fixed plate flat and the moving plate convex. The

surfaces of both plates could be plain or corrugated. The moving plate applies the force of impact

on the particles held against the stationary plate. Both plates are bolted on to a heavy block. As

the reciprocating action removes the moving jaw away from the fixed jaw the broken rock

particles slip down, but are again caught at the next movement of the swinging jaw and crushed.

This process is repeated until the particle sizes are smaller than the smallest opening between the

crusher plates at the bottom of the crusher (the closed set). For a smooth reciprocating action of

the moving jaws, heavy flywheels are used in both types of crushers.

Dowding Charles H. [7] designed jaw plates to reduce efforts to decrease energy consumed

in crushing have lead to consideration of decreasing the weight of the swing plate of jaw crushers

for easily crushed material. This paper presents the results of an investigation of the feasibility of

using point load-deformation-failure (PDF) relationships along with interactive failure of rock

particles as a model for such a weight reduction. PDF relationships were determined by point-

loading various sizes of materials: concrete mortar, two types of limestone, amphibolites and

taconite. Molling [7], who proposed this hypothetical distribution, was only concerned with the

total loading force. The parameter which most controls the design of the swing plate is the load

distribution. Instrumentation of toggle arms in has since led to correlation of measured with rock

type. Ruhl [7] has presented the most complete consideration of the effect of rock properties on

Q and the toggle force. His work is based upon the three-point loading strength of the rock,

which he found to be one-sixth to one eleventh the unconfined compressive strength. He

calculated hypothetical toggle forces based upon the sum of forces necessary to crush a

distribution of regular prisms fractured from an initial cubical rock particle. These approaches

involved both maximum resistance and simultaneous failure of all particles and thus neither can

lead to an interactive design method for changing stiffness (and weight) of the swing plate. In

this study point-loading of cylinders are undertaken to model behavior of irregular rock particles.

15

Berry P. et al [8] studied the laws of mechanics and constitutive relations concerning rock

breakage characteristics. The simulated results are consistent with the general description and

experimental results in the literature on particle breakage. A descriptive and qualitative particle

breakage model is summarized as the following: at the first loading stage the particle is stressed

and energy is stored as elastic strain energy in the particle. A number of randomly distributed

isolated fractures are initiated because of the heterogeneity.

Weiss N.L. [9] work is on the liner of a jaw crusher is an interface for analyzing the

crushing force, on which the crushing force occurs, in other words, the directly contact and the

interaction between the material and the liner occur there. So the interface has great effect on the

crushing feature of jaw crusher. The liner is one of the curves in the cross-section of the couple

plane, which is also given a definition as one of the coupler curves in a four bar crank-rocker

model.

Niles I. L. [10] showed that point-load failure of a sphere was equal to that of a point-

loaded ellipsoid. Therefore, ultimate point loads on spheres will be approximately equal to

ultimate point loads on cylinders (or discs). For both the ellipsoids and the cylinders, the excess

volume outside the spherical dimensions does not change the circular failure surface parallel to

the smallest dimensions of the body. This circular failure surface for the sphere and cylinder is

shown by the jagged lines on the two shapes. These authors and others also compared disc and

irregular particle point-load strengths from tests on dolomite, sandstone and shale and found the

point load strength of the disk and irregularly shaped particles to be equal. Thus, the properties

determined from point-loading of discs or cylinders are appropriate for the point-loading of

irregular particles.

Georget Jean-Pirre and Lambrecht Roger [11] invented jaw crushers comprising a frame,

a stationary jaw carried by the frame a mobile jaw associated with the stationary jaw and

defining a crushing gap therewith; an eccentric shaft supporting one end of the frame and a

connecting rod or toggle supporting the other mobile jaw end on the crossbeam. The position of

the crossbeam in relation to the frame is adjustable to change the distance between the jaws i.e.

the size of crushing gap. A safety system permits the mobile jaw to recoil when the pressure it

exerts on the connecting rod exceeds a predetermined value, for example because an unbreakable

piece is in the crushing gap. In the illustrated jaw crusher, the crossbeam is pivotally mounted on

the frame for pivoting about an axis parallel to the shaft and the safety system acts; on the

16

crossbeam to prevent it from pivoting when the force applied by the mobile jaw to the crossbeam

remains below a predetermined value.

Pollitz H.C.[12] presents invention concerns an improved design of stationary and

movable jaw plates for jaw type crusher which minimizes warping of the jaws and increases their

life more particularly the present invention concerns an improved structure for mounting the

stationary jaw plate to the crusher frame and for increasing the rigidity and life of both plates.

Zhiyu Qin, Ximin Xu [13] indicated that the relationship between the increasing rate of holdup

and the material-feeding rate were examined. From the results, the maximum crushing capacity

was defined as the maximum feed rate where holdup did not change with time and remained at a

constant value.

Qin Zhiyu [14] studied different positions of liners in the coupler plane have different

moving features, the motion of points along the liners in the computing domain is quite different

from that of them in the straight-line coupler of the simple four bar crank-rocker model.

Therefore, it is necessary to consider motion differences caused by different liner positions and

their motion features to select a coupler curve as the swing liner with good crushing character.

Cao Jinxi [14] worked on the certain domain, called the liner domain, of the coupler plane is

chosen to discuss the kinetic characteristic of a liner or a crushing interface in the domain. Based

on the computation and the analysis of the practical kinetic characteristic of the points along a

liner paralleling to the direction of coupler line, some kinematics arguments are determined in

order to build some kinetic characteristic arguments for the computing, analyzing and designing.

Lytwynyshyn G. R [15] reported that the slow compression test was the most efficient

method of particle fragmentation with impact loading being approximately 50% efficient, whilst

the ball mill was considered to be approximately 15% as efficient as the slow compression test.

Krogh undertook drop weight tests on small samples of quartz with the impact speed in the range

0.64-1.9 m/s, but with constant impact energy. It was found that the probability of breakage of

each individual particle was not influenced by impact speed nor was the size distribution of the

fragments produced.

Gabor M. Voros [16] presents the development of a new plate stiffener element and the

subsequent application in determine impact loads of different stiffened plates. In structural

modeling, the plate and the stiffener are treated as separate finite elements where the

displacement compatibility transformation takes into account the torsion – flexural coupling in

the stiffener and the eccentricity of internal forces between the beam – plate parts. The model

17

becomes considerably more flexible due to this coupling technique. The development of the

stiffener is based on a general beam theory, which includes the constraint torsional warping

effect and the second order terms of finite rotations. Numerical tests are presented to demonstrate

the importance of torsion warping constraints. As part of the validation of the results, complete

shell finite element analyses were made for stiffened plates.

Kadid Abdelkrim [17] carried out investigation to examine the behavior of stiffened

plates subjected to impact loading. He worked to determine the response of the plates with

different stiffener configurations and consider the effect of mesh dependency, loading duration,

and strain-rate sensitivity. Numerical solutions are obtained by using the finite element method

and the central difference method for the time integration of the non-linear equations of motion.

Special emphasis is focused on the evolution of mid-point displacements, and plastic strain

energy. The results obtained allow an insight into the effect of stiffener configurations and of the

above parameters on the response of the plates under uniform blast loading and indicate that

stiffener configurations and time duration can affect their overall behavior.

Jaw plates used in modern crushing operations are fabricated almost exclusively from what

is generally known as Hadfield manganese steel [19], steel whose manganese content is very

high and which possesses austenitic properties. Such jaw plates are not only extremely tough but

are also quite ductile and work-harden with use. Under the impact of crushing loads “flow” of

the metal at the working surface of the plate occurs in all directions. This “flow” occurs chiefly

in the central area of the plate, particularly the lower central area, because the lower portion of

the plate does very substantially more work than the upper portion. This is particularly true in

case of the stationary jaw, which, as well known receives the greater wear in operation. If the

“flow” is not compensated for, the jaw will distort or warp, particularly in its more central area,

so that it will no longer contact its seat. Thus crushing loads will cause it to flex with consequent

decrease in crushing efficiency and increase in wear both of the jaw itself and particularly its

seat.

CHAPTER -3

THEORETICAL ANALYSIS AND DATA COLLECTION

18

3. THEORETICAL ANALYSIS AND DATA COLLECTION

3.1 Introduction to Kinematics of the Machines

3.1.1 Study of Machines:

In general the study of a Machine involves problems of three distinct kinds. We may first

of all consider from a geometrical point of view the motion of any part of the machine with

reference to any other part, without taking account of any of the forces acting on such parts. Or,

the action of the forces impressed on the parts of the machine, and of the forces due to its own

inertia or to the weight of its parts, may be dealt with, and the resulting transformations of energy

may be determined. A third branch of the theory of machines treats of the action of these loads

and forces in producing stresses and strains in the materials employed in the construction of the

machine, and discusses the sizes, forms, and proportions of the various parts which are required

either to insure proper strength while avoiding waste of material, or to make the machine capable

of doing the work for which it is being designed.

The science dealing with the first-named class of problem is termed the Kinematics of

Machines, which we may define as being that science which treats of the relative motion of the

parts of machines, without regard to the forces producing such motions, or to the stresses and

strains produced by such forces.

3.1.2 Kinematics of Machines:

With this limitation, in the case of almost all bodies forming portions of machines, it is

possible to neglect any deformation they may undergo in working, and in studying the

Kinematics of Machines we may at once apply to machine problems the results obtained by the

study of the motion of rigid bodies. Important exceptions will present themselves to the reader's

mind; for example, ropes, belts, and springs cannot be considered kinematically as being rigid,

and many mechanical contrivances involve the use of liquid or gaseous material. Such cases as

these will be considered later.

By the term Machine we may understand a combination or arrangement of certain

portions of resistant material, the relative motions of which are controlled in such a way that

some form of available energy is transmitted from place to place, or is transformed into another

desired kind. This definition includes under the head of Machines all contrivances which have

for their object the transformation or transmission of energy, or the performance of some

19

particular kind of work, and further implies that a single .portion of material is not considered as

a machine. The so-called simple machines in every case involve the idea of more than one piece

of material.

A combination or arrangement of portions of material by means of which forces are

transmitted or loads are carried without sensible relative motions of the component parts is called

a structure.

The term Mechanism is often used as an equivalent for the word Machine. It is, however,

preferable to restrict its use somewhat, and to employ the word to denote simply a combination

of pieces of material having definite relative motions, one of the pieces being regarded as fixed

in space. Such a mechanism often represents kinematically some actual machine which has the

same number of parts as the mechanism with the same relative motions. The essential difference

is that in the case of a machine such parts have to transmit or transform energy, and are

proportioned and formed for this end, while in a mechanism the relative motion of the parts only

is considered. We may look upon a mechanism, then, as being the ideal or kinematic form of a

machine, and our work will be much simplified in most cases if we consider for kinematic

purposes the mechanism instead of the machine. Such a substitution is also of the greatest service

in the comparison and classification of machines; we shall find in this way that machines, at first

sight quite distinct, are really related, inasmuch as their representative mechanisms consist of the

same number of parts having similar relative motions, and only differing because a different

piece is considered to be fixed in each case.

3.1.3 Classification of Mechanisms:

In attempting to classify mechanisms, which are made up of various kinds of links and

involve so many kinds of pairing, we are impressed with the magnitude and complexity of the

task. It may be said, in fact, that up to the present no wholly satisfactory kind of machine

classification has been proposed to consider mechanisms under three heads.

1. Those involving only plane motion. These may be called shortly Plane Mechanisms, and

form by far the most important and numerous classes.

2. Mechanisms involving spheric motion, or, more briefly, Spheric Mechanisms.

3. Chains the relative motion of whose links is neither plane nor spheric, but of greater

complexity.

20

It is, however, to be understood that a mechanism of the third kind may contain certain

links whose motion is plane or spheric, while any of them may include examples of both lower

and higher pairing.

A well-known instance of a spheric mechanism is Hooke’s joint, the characteristic

property of such chains being that the axes of the turning pairs they contain meet in a point. In

the third class the most common examples are screw mechanisms.

There is another method of classifying machines according to their geometrical

properties, and according to the methods necessary for determining the various virtual centres of

their links. From this it follows that in such mechanisms, having given the whole mechanism in

one position, we can find geometrically all its other possible positions, and: the virtual centre of

each link relatively to every other. Mechanisms not possessing these properties belong to higher

orders, and are of comparatively infrequent occurrence.

3.1.4 Four-Bar Linkage

A four-bar linkage or simply a 4-bar or four-bar is the simplest movable linkage. It

consists of four rigid bodies (called bars or links), each attached to two others by single joints or

pivots to form a closed loop. Four-bars are simple mechanisms common in mechanical

engineering machine design and fall under the study of kinematics. If each joint has one

rotational degree of freedom (i.e., it is a pivot), then the mechanism is usually planar, and the 4-

bar is determinate if the positions of any two bodies are known (although there may be two

solutions). One body typically does not move (called the ground link, fixed link, or the frame), so

the position of only one other body is needed to find all positions. The two links connected to the

ground link are called grounded links. The remaining link, not directly connected to the ground

link, is called the coupler link. In terms of mechanical action, one of the grounded links is

selected to be the input link, i.e., the link to which an external force is applied to rotate it. The

second grounded link is called the follower link, since its motion is completely determined by the

motion of the input link.

Grashof’s law is applied to pinned linkages and states; The sum of the shortest and

longest link of a planar four-bar linkage cannot be greater than the sum of remaining two links if

there is to be continuous relative motion between the links. Fig3.1 shows the possible types of

pinned, four-bar linkages.

21

Fig.3.1 Types of four-bar linkages, s = shortest link, ℓ = longest link

3.2 Jaw Crusher as a Crank- Rocker Mechanism:

Mechanism of a typical single toggle jaw crusher can be treated as a crank-rocker

mechanism of a four-bar linkage having; frame as a fixed link, crank as an eccentric shaft, liner

as coupler and toggle plate as follower as shown in the Fig3.2. The calculation parameters of the

PE400×600 are shown in Table 3.1.

r(mm) l(mm) k(mm)

12 1085 455

Table 3.1: PE400*600 Jaw Crusher Calculation Parameters

AB = Crank (r)

BC = Length of the liner (l)

CO = toggle plate length (k)

AO = frame or fixed link

Toggle plate one end is connected to frame (O) and other end is connected to the

movable jaw(c) as shown in the Fig.3.2.The angles Ө and Ф represents the angle of liner and

crank making with vertical.

Dimensions and operating parameters when considering the jaw crusher of Fig.3.2, there

are variables of the feed that define the important machine dimensions.

� The feed particle sizes of interest are:

1.The size of particle that enters the crusher

2.The size of particle that can be nipped

3.The size of particle that can fall through the chamber at any time

4.The size of particle that can fall through the chamber when the jaws are open as wide as

possible.

� The dimensions defined by those particle sizes are (Fig

1.The gape - the distance between the jaws at the feed opening

2.The closed side set (CSS)

cycle (minimum discharge aperture)

3.The open side set (OSS)

4.The throw – the stroke of the swing jaw and the difference between OSS and CSS.

3.3 Choosing the Points along the Liner for Computing:

A liner of jaw crusher is an interface for analyzing the

crushing force occurs, in other

material and the liner occur there. So the interface has great

crusher. The liner is one of the curves in

given a definition as one of the coupler curves in a

positions of liners in the coupler plane have different moving features, the

the liners in the computing domain is

of the simple fourbar crank

differences caused by different

as the swing liner with good crushing character.

Based on the fourbar crank

calculating is shown in Fig.3.3.

is UCV. Although a real shape and position of a fixed working

22

The dimensions defined by those particle sizes are (Fig.3.2 ):

the distance between the jaws at the feed opening

The closed side set (CSS) - the minimum opening between the jaws during the crushing

cycle (minimum discharge aperture)

The open side set (OSS) – the maximum discharge aperture

the stroke of the swing jaw and the difference between OSS and CSS.

Choosing the Points along the Liner for Computing:

A liner of jaw crusher is an interface for analyzing the crushing

orce occurs, in other words, the directly contact and the interaction between the

material and the liner occur there. So the interface has great effect on the crushing feature of jaw

of the curves in the cross-section of the couple plane, which is

given a definition as one of the coupler curves in a fourbar crank-rocker model. Since different

liners in the coupler plane have different moving features, the

ners in the computing domain is quite different from that of them in the straight

the simple fourbar crank-rocker model. Therefore, it is necessary to consider motion

differences caused by different liner positions and their motion features to select a coupler

as the swing liner with good crushing character.

Based on the fourbar crank-rocker model, the system sketch of jaw crusher fo

3.3. The global static coordinate is XOY and the dynamic coordinate

Although a real shape and position of a fixed working liner is usually determined by a

Fig.3.2 Jaw Crusher sketch(12)

the minimum opening between the jaws during the crushing

the stroke of the swing jaw and the difference between OSS and CSS.

ng force, on which the

words, the directly contact and the interaction between the

effect on the crushing feature of jaw

section of the couple plane, which is also

rocker model. Since different

motion of points along

quite different from that of them in the straight-line coupler

necessary to consider motion

to select a coupler curve

sketch of jaw crusher for

global static coordinate is XOY and the dynamic coordinate

liner is usually determined by a

23

suspension point of the jaw crusher, computation of a liner will be done on the one of chosen

curves in the liner domain. Thus with different position on the liner, each computing point on it

liners will arrive at the limit position at different time. However it is well known that a practical

crushing force exerted on fractured material is in the normal direction of the liner. The normal

direction of each point in the liner changes in one operation cycle. So a distance between the

limit positions in normal direction of those points is quite different from that of the displacement

of horizontal motion.

In order to describe the kinematic characteristics of the points in the liner domain, the

single toggle jaw crusher PE400x600 is taken as example to compute and analyze the distributed

kinematic characteristic. The calculation parameters of the PE400×600 are shown in Table3.1. In

order to illustrate the motion of the points in liner domain, it is needed to define the liner domain.

One plane along the coupler BC is selected and is divided into 10 equal parts as shown in the

Fig.3.3. So there are 11 points selected to be calculate in the V direction for a certain U and the

eccentric shaft is rotating at a speed of 300rpm. The position of the eccentric shaft with respect to

global co-ordinates XOY is A(a , b) is located at a=45.3 & b=815.7. With the points for

computing and the liner domain chosen as above mentioned, computing results are shown in

follows.

Fig.3.3 Points track along the liner

-300

-150

0

150

300

450

600

750

900

0 150 300 450

y(m

m)

x(mm)

3.4 Movement Computation and Feature Analysis of Points:

The mechanism of the jaw crusher is shown in Fig.3.2; g

crank AB is clockwise.

Where ∅= Crank angle made by vertical

θ= Angle between

By rotating crank (∅) from 00

0 36 72 108

18.898 19.473 19.994 20.249

Table 3.2: variation of nip angle with crank angle

Given the position of any point in

coordinate XOY is (x, y) as shown in Fig.

As mentioned above BC l=

By observing Fig. sin(90 )AK r= −

cos(90 )BK r= −

And ' cosLP u θ= , ' sinPP u=

MN a BK= −

sina r φ= −

( )sinNL BC LC θ= −

( )sinl v θ= −

2 2 2

2

( ) ( 1)( 1)sin

mn mn n m

nθ − + − + −

=

cos sinm nθ θ= +

2 2 2 2 2a b r l k r a bm

+ + + − − +=

sin

cos

a rn

b r

φφ

−=−

24

Movement Computation and Feature Analysis of Points:

e jaw crusher is shown in Fig.3.2; given the rotation direction of

= Crank angle made by vertical

een two plates ≤ 900 and

………………

………………

……………

…………….. 0-3600 the variation of nip angle (θ) is shown in Table 3.2.

108 144 180 216 252 288

20.249 20.146 19.742 19.192 18.696 18.43

Table 3.2: variation of nip angle with crank angle

Given the position of any point in dynamic coordinate UCV is (u, v)

coordinate XOY is (x, y) as shown in Fig.3.4.

BC l , AB r= .

sin(90 )AK r φ= −,

cos(90 )BK r φ= −.

' sinPP u θ ,

θ

2 2 2

2

( ) ( 1)( 1)

1

mn mn n m

n

− + − + −+

2 2 2 2 2

2

2 ( sin cos )

1

a b r l k r a b

n

φ φ+ + + − − ++

Fig.3.4 Point consideration in dynamic coordinate

Movement Computation and Feature Analysis of Points:

iven the rotation direction of the

(3.1)

(3.2)

(3.3)

(3.4)

) is shown in Table 3.2.

324 360

18.43 18.501 18.898

coordinate UCV is (u, v) and in global

Fig.3.4 Point consideration in dynamic coordinate

25

'AP AK K P= +

' 'K P BN PP= −

'AP AK BN PP⇒ = + −

cos ( )cos sinAP r l v uφ θ θ⇒ = + − −

Therefore horizontal displacement:

'x MN NL LP= + +

sin ( )sin cosx a r l v uφ θ θ∴ = − + − +

……………… (3.5)

And vertical displacement:

y b AP= −

cos ( )cos siny b r l v uφ θ θ∴ = − − − + ……………….. (3.6)

By rotation of the crank for one complete cycle, the variations of horizontal and vertical

displacements for the 11 points along the liner are shown in Fig.3.5 & Fig.3.6.

Fig.3.5 Horizontal Displacements Fig.3.6 Vertical displacements

The track of the sixth point is magnified and shown in Fig.3.7. The displacement variations of the sixth point are shown in Fig3.8 & Fig.3.9. By observing the Fig.3.7, that the path of any point on the liner is analogous to an ellipse.

0

50

100

150

200

250

300

350

400

450

0 120 240 360

x(m

m)

Ф(Degrees)

1

2

3

4

5

6

7

8

9

10

11

-300

-100

100

300

500

700

900

0 120 240 360

mm

Ф(degrees)

1

2

3

4

5

6

7

8

9

10

11

26

And the velocity of the points can be express as following equations:

Since ……………… (3.7)

Velocity in X-direction (VX) can be expressed with respect to crank rotation as

X

dxv

dt=

( )cos ( )sin sind

u l v a rd

θ θ φ ωφ

= + − + −

……………… (3.8)

The horizontal velocity variation for 11 points along the liner or swinging jaw plate

relative to the angle parameter Ф is shown in Fig.3.10.

Fig.3.10 Horizontal velocities

280

290

300

310

320

215 220 225 230 235

y(m

m)

x(mm)

216

220

224

228

232

0 120 240 360m

mФ(Degrees)

280

290

300

310

320

0 120 240 360

mm

Ф(Degrees)

-450

-300

-150

0

150

300

450

0 120 240 360

vx

m

m/s

Ф(Degrees)

1

2

3

4

5

6

7

8

9

10

11

( sin )cos ( cos )sin

sin ( cos )

d r a l l b

d l a r b r

θ θ φ θ φφ φ φ

+ + −= − + −

( )cos cos sinX

d dv l v r u

d d

θ θθ φ θ ωφ φ

= − − −

Fig.3.7 6th Point Track Fig.3.8 6th Point horizontal Fig.3.9 6th Point Vertical Displacement Displacement

dx d

d dt

φφ

=

27

And velocity in Y-direction (Vy) can be expressed with respect to crank rotation as

X

dxv

dt=

dx d

d dt

φφ

=

( )cos ( )sin sin

du l v a r

dθ θ φ ω

φ= + − + −

( )sin sin sinY

d dv l v r u

d d

θ θθ φ θ ωφ φ

= − + +

……………… (3.9)

The vertical velocity variation for 11 points along the liner or swinging jaw plate

relative to the angle parameter Ф is shown in Fig.3.11.

Fig.3.11 Vertical velocities

It can found that velocity in U-direction (vu) and velocity in V- direction (vv) as shown in

equations 3.10 & 3.11.

( ) cos( )U

dv l v r

d

θ φ θ ωφ

= − − +

……………… (3.10)

sin( )V

dv u r

d

θ φ θ ωφ

= + +

……………… (3.11)

It is shown in equation 3.11 that the point with the same V component has the same

velocity component in the U direction, i.e., the U component has no effect on the velocity

component in the U direction. The variation of the velocity component in U direction relative to

the angle parameter ∅ is shown in Fig.3.12. It is obvious that the amplitude of the velocity

-600

-400

-200

0

200

400

600

0 120 240 360

vy

mm

/s

Ф(Degrees)

1

2

3

4

5

6

7

8

9

10

11

28

variation is minimal for the points at the suspending point zone. The variation of the initial phase

has a certain law.

Fig.3.12 U-directional Velocities

It is shown in equation3.12 that the point with the same U component has the same velocity

component in the V direction. In other words the V component has no effect on the velocity

component in the V direction. The variation of the velocity component in V-direction relative to

angle ∅ is shown in Fig.3.13. It is obvious that the amplitude of the velocity variation is

decreasing with the decreasing U component. The variation of the initial phase has a certain law.

Therefore the accelerations along the X direction (ax) and Y direction (ay) can also be found

as follows.

XX

dva

dt= Xdv d

d dt

φφ

=

-600

-400

-200

0

200

400

600

0 120 240 360

vu

mm

/s

Ф(Degrees)

1

2

3

4

5

6

7

8

9

10

11

-450

-300

-150

0

150

300

450

0 120 240 360

mm

/s

Ф(Degrees)

1

2

3

4

5

6

7

8

9

10

11

Fig.3.13 V-directional Velocities

29

2( )cos cos sind d d

l v r ud d d

θ θθ φ θ ωφ φ φ = − − −

[ ] [ ]22

2( )cos sin ( )sin cos sin2

d da l v u l v u rx dd

θ θθ θ θ θ φ ωφφ

∴ = − − − − + + ….. (3.12)

YY

dva

dt= Ydv d

d dt

φφ

=

2( )sin sin sind d d

l v r ud d d

θ θθ φ θ ωφ φ φ = − + +

[ ] [ ]22

2( )s s ( ) s sin s2

d da l v in uco l v co u rco

y dd

θ θθ θ θ θ φ ωφφ

∴ = − + + − − + ….. (3.13)

Equation 3.12 and 3.13 shows the horizontal and vertical accelerations. Fig.3.14. and

Fig.3.15 represents the variation of accelerations in horizontal and vertical directions relative to

the crank angle∅ varying from 00- 3600.

Fig.3.14 Horizontal accelerations Fig.3.15 Vertical accelerations

Equation 3.14 and 3.15 shows the accelerations in U-direction and V-direction. Fig.3.16.

and Fig.3.17 represents the variation of accelerations in U-direction and V-direction relative to

the crank angle∅.

-1.5E+04

-1.0E+04

-5.0E+03

0.0E+00

5.0E+03

1.0E+04

1.5E+04

0 120 240 360

ax

mm

/s2

Ф(Degrees)

1

2

3

4

5

6

7

8

9

10

11

-2.0E+04

-1.5E+04

-1.0E+04

-5.0E+03

0.0E+00

5.0E+03

1.0E+04

1.5E+04

2.0E+04

0 120 240 360

ay

mm

/s2

Ф(Degrees)

1

2

3

4

5

6

7

8

9

10

11

30

UU

dva

dt=

Udv d

d dt

φφ

=

2( )sin sin sind d d

l v r ud d d

θ θθ φ θ ωφ φ φ = − + +

22( ) sin( ) 1U

d da l v r

d d

θ θθ φ ωφ φ

∴ = − + + +

……………… (3.14)

VV

dva

dt= Vdv d

d dt

φφ

=

2sin( )d d

u rd d

θ θ φ ωφ φ = + +

22s( ) 1V

d da u rco

d d

θ θθ φ ωφ φ

∴ = + + +

……………… (3.15)

Fig.3.16 U-directional accelerations Fig.3.17 V-directional accelerations

-1.5E+04

-1.0E+04

-5.0E+03

0.0E+00

5.0E+03

1.0E+04

1.5E+04

0 60 120 180 240 300 360

au

mm

/s2

Ф(Degrees)

1

2

3

4

5

6

7

8

9

10

11

-1.5E+04

-1.0E+04

-5.0E+03

0.0E+00

5.0E+03

1.0E+04

1.5E+04

0 120 240 360

mm

/s2

Ф(Degrees)

And

31

3.5 Squeezing Process & Particle Breakage

3.5.1 Fractured Size Distribution:

With the energy intensity increasing, there are three fracture mechanisms under

compression condition, as is shown in Fig.3.19. The breakage process due to the point contact

loading that occurs between the plates of a jaw crusher and a particle is illustrated in Fig.3.18.

The particle fracture mechanism in jaw crusher chamber is the mixture of the cleavage and the

abrasion. The abrasion fracture is caused with the localized too much energy input to the area

directly under the loading points and the friction between the jaw plates and the particle. The

areas directly below the loading contacts fail in compression producing abrasion fracture.

Abrasion can be thought as type of shatter fracture.

Fig.3.18 Fracture caused by compression crushing [12] Fig.3.19 Particle fracture mechanism

The distribution of the particle sizes after fracture is dependent on the fracture

mechanisms occurring as a result of particle loading. For a given material, as particle size

decreases strength increases. This is due to the distribution of flaws within the material. Fracture

initiates from the flaw independently of all other flaws within the particle. Since the mechanisms

of fracture also control the distribution of progeny particle sizes and specific fracture

mechanisms produce specific fragment size. The energy criterion states that enough potential

energy must be released in order to overcome a material’s resistance to crack propagation,

requiring an increase in the work done by external forces acting on the material. This is the

amount of input energy to reducing the size of particle. The amount of size reduction or the size

distribution resulting from fracture is dependent upon the presence and distribution of cracks.

32

3.5.2 Squeezing Process:

In the common sense the nipped particle should be compressed and failed in tension

stress in the jaw crusher chamber. But in practice a sliding motion between the jaw plates and the

particle is inevitable. It is because that the moving jaw has the vertical movement relative to the

fixed jaw during the squeezing process. Sometimes sliding is accompanied with rolling motion

of the particle, which is determined by the geometry of the particle and the chamber. Because the

sliding motion between the moving and fixed jaw plates and the particle is a key factor to the jaw

plates wear, it is necessary to analyze this process.

The force on the particle during the squeezing process is shown in the Fig.3.20. Since the

horizontal and the vertical velocities of the moving jaw are variable during the squeezing

process, the forces on the particle are also variable in different stages in the crushing chamber.

When the component of the vertical velocity in the moving jaw plate direction is bigger than that

of the horizontal velocity in the same direction, the forces on the particle are shown in Fig.3.20

(a). When the component of the vertical velocity in the jaw plate direction is smaller than that of

the horizontal velocity, the forces on the particle are shown in Fig.3.20 (b). Because the

gravitational force is much smaller than others, it can be ignored.

Where N1, N2 represents the normal reactions of the moving and fixed jaw plates on the

crushing material and f1, f2 represents the frictional force between the jaw plates and the crushing

material.

The angle α = 900- Nipping angle

(a) (b)

Fig.3.20 Forces on particle during crushing

33

Considering equilibrium for Fig (a)

Equilibrium in horizontal direction:

……… (3.16)

Equilibrium in vertical direction:

……… (3.17)

1 1 2s sin ' 0N co N Nα µ α µ⇒ + − = ……… (3.18)

Given that the slide first takes place between the particle and the moving jaw plate. The

friction coefficient isµ.

……… (3.19)

The friction coefficient between the particle and the fixed jaw plate will be µ’

……… (3.20)

By equations (3.16) & (3.19)

1 1 2sin cos 0N N Nα µ α− − = ……… (3.21)

( )2 1 sin cosN N α µ α⇒ = − ……… (3.22)

From equation (3.18)

……… (3.23)

..…… (3.24)

…… (3.25)

It is inconsistent to the assumption

Given that the slide first takes place between the particle and the fixed jaw plate and the

friction coefficient isµ.

..……. (3.26)

The friction coefficient between the particle and the moving jaw plate will be µ’.

……. (3.27)

Form equation (3.16) & (3.27)

……. (3.28)

1 1 2sin cos 0N f Nα α− − =

1 1 2s sin 0N co f fα α+ − =

1 1f Nµ⇒ =

2 2'f Nµ⇒ =

( )( )

s sin' 0

sin cos

co α µ αµ

α µ α+

= >−

( )( )

s sin'

sin cos

co α µ αµ µ µ

α µ α+

⇒ − = −−

2 cos cos0

sin cos

µ α αα µ α

− −= <−

2 2f Nµ⇒ =

1 1'f Nµ⇒ =

( )2 1 sin 'cosN N α µ α= −

34

Form equation (3.17) & (3.26)

……. (3.29)

∴ The friction coefficient between the particle and the moving jaw plateµ’ can be found from

equations (3.28) & (3.29)

…… (3.30)

And

……. (3.31)

……. (3.32)

It is rational.

So the slide distance between the particle and the fixed jaw plate is more than that

between the particle and the moving jaw plate during the squeezing process.

3.6 Introduction to Design of Jaw Plates

Recently, concern for energy consumption in crushing has led to the consideration of

decreasing the weight (and consequently the stiffness) of the swing plate of jaw crushers to

match the strength of the rock being crushed. An investigation of the energy saving of plate rock

interaction when point load deformability and failure relationships of the rock are employed to

calculate plate stresses. Therefore some line and unconfined compression tests were conducted to

determine typical point load-deformation relationships for a variety of rock types. Secondly, a

numerical model of the swing plate A as shown in Fig.3.23 has been developed.

Fig.3.21 Elevation View of Jaw Crusher [6]

1 2( s 'sin ) 0N co Nα µ α µ⇒ + − =

( )( )

s sin'

sin cos

co α µ αµ

α µ α− +

=+

( )( )

s sin'

sin cos

co α µ αµ µ µ

α µ α− +

− = −+

2 cos cos0

sin cos

µ α µ αα µ α

+= >+

35

The swing plate A is idealized as shown in Fig.3.23 (a) as a unit width beam loaded at a

number of points by different sized particles. Each row of uniformly sized particles in Fig. 3.23

(b) is idealized as one point load on the unit width model of the swing plate. Because of the

interactive nature of this model, the failure of any row of particles permits redistribution of

stresses within the beam.

AB

Fig.3.22. Idealization of particles within jaw crusher.

(a) Cross section CC (b) Plan View of Plate A

Fig.3.23. Modeling of particles within jaw crusher.

36

3.6.1 The load distribution along the swing plate

The parameter which most controls the design of the swing plate is the load distribution,

shown in Fig.3.24.This hypothetical distribution, was only concerned with the total loading force

(Q). Instrumentation of toggle arms in Germany has since led to correlation of measured Q with

rock type. The most complete consideration of the effect of rock properties on Q and the toggle

force (T). The hypothetical toggle forces based upon the sum of forces necessary to crush a

distribution of regular prisms fractured from an initial cubical rock particle. These approaches

involved both maximum resistance and simultaneous failure of all particles.

Fig.3.24 Load distribution along plate A only.

Normally, the stiffness and dimensions of swing plates are not changed with rock type and

all plates are capable of crushing rock such as taconite. Only the facing of the swing plate is

changed with rock type, to account for changes in abrasiveness or particle shape. For instance,

ridged plates are employed with prismatic particles both to stabilize the particles and to ensure

the point-loading conditions. Communications with manufacturers of jaw crushers have revealed

that no consideration is currently given to force displacement characteristics of the crushed rocks

in the design of swing plates.

Consideration of the two particles between the crusher plates in Fig.3.24 reveals the

importance of the point-load failure mechanism. As a rock tumbles into position it will catch on

a corner of a larger diameter and thus will be loaded at two ‘points’ of contact. Throughout the

paper, ‘point’ describes contact over a small and limited region of the circumference of the

particle.

37

3.6.2 Modeling irregular particle behavior with that of cylinders

In this study point-loading of cylinders (or discs) are undertaken to model behavior of

irregular rock particles. Modeling irregular particle behavior with that of cylinders can be shown

to be appropriate by consideration of work presented by Hiramatsu and Oka. The plate

idealization may be replaced by the point load shown in Fig.3.25.

They also showed that point-load failure of a sphere was equal to that of a point-loaded

ellipsoid. Therefore, ultimate point loads on spheres will be approximately equal to ultimate

point loads on cylinders (or discs). For both the ellipsoids and the cylinders, the excess volume

outside the spherical dimensions does not change the circular failure surface parallel to the

smallest dimensions of the body. This circular failure surface for the sphere and cylinder is

shown by the jagged lines on the two shapes in Fig.3.25. These results compared with disc and

irregular particle point-load strengths from tests on andecite, dolomite, sandstone and shale and

found the point load strength of the disk and irregularly shaped particles to be equal. Thus, the

properties determined from point-loading of discs or cylinders are appropriate for the point-

loading of irregular particles.

As has been shown by numerous workers [7], the maximum point load, P, is related to the

tensile strength (St) as shown in eqn. (3.32).

2tS d

P=X ……….. (3.32)

Where d is diameter of specimen and X is a proportionality factor. The proportionality factor X

has been reported by the above investigators to range between 0.96 and 0.79. The measurements

of the deformability of small iron ore pellets and glass beads when crushed between two plates

Irregular Particle Sphere Particle Cylinder Particle

Fig.3.25. Comparison of plate and point-loaded particles.

38

obtained. The load-deformation relationships of both materials displayed deformation hardening

in the initial stages of loading as predicted by the Hertzian theory for the behavior of contacting

spheres. According to the Hertzian theory, the total diametrial deformation (D) of a sphere

loaded by two plates (spheres of infinite radius) is given by:

( ) 1/32 2

2r

P 1-n9D = 2 .

16 RE

……….. (3.33)

Where P is the point load, R is the radius of rock particles, E, is Young’s modulus of rock, and ν

is Poisson’s ratio. For v between 0.25and 0.33, eqn. (3.33) reduces to

2/3

1/3 2/3r

PD=1.6

R E ……….. (3.33)

Therefore any given sphere will deform according to a deformation hardening power law:

aD=KP ……….. (3.34)

Where a is a constant, for completely elastic behavior it is 2/3.

3.7 Experimental Data Collection

3.7.1 Point load deformation and failure (PDF) data for materials

Point load deformation and failure (PDF) data were obtained for the five materials: sand-

cement mortar, fragmental limestone, dolomitic limestone, taconite and amphibolites (closely

banded gneiss) have shown in Table 3.3 with their major properties.

Table 3.3 Materials tested [7]

Material E (MPa) q� (Mpa) Location Mineralogy, Texture

Mortar 9.7 20.7 Made in laboratory

Chicago Lyons, IL

Northern Minnesota

Massachusetts

Sand and cement

mixture fragmental,

porous Dolomitic

siliceous, finely

grained crystalline.

Fragmental limestone 30.3 54.5

Dolomitic limestone 48.3 151.7

Taconite 41.4 234.4

Amphibolites 33.6 124.1

39

3.7.2 Effects of size on both strength and deformability

Cylinders ranging in size from 25 mm (1 in) to 150 mm (6 in) in diameter were point-

loaded to investigate the effects of size on PDF properties (both strength and deformability).

Knowledge of this size effect is necessary to model accurately the crushing behavior of the range

of particle sizes found in jaw crushers Table 3.4 summarizes the results of the 30 point-load tests

to determine the PDF relationships. To compare PDF data for a variety of diameters, the force

and displacement at failure, �� and �, were normalized. The normalized failure load (��) is the

tensile strength given by eqn.1 (X = 0.79) and is relatively independent of size. Deformation at

failure (�) was normalized through division by the original diameter to obtain (�). The power

law deformation descriptors, K and a in Table 3.3, were found by plotting non-normalized PDF

data on log-log paper. Average values of the normalized failure loads and deformation and K and

a are given in Table 3.4.

T

Fig.3.26. Comparison of the effect of size on point load at failure.

The point load-deformation and failure (PDF) relationships display definite Hertzian

behavior. This upward curvature is evident in the comparison of typical rock PDF behavior in

Fig. 3.26. These typical relationships are based upon the 28 mm specimens of taconite,

amphibolites and dolomitic limestone and the 56-mm specimens of fragmental limestone.

0

2

4

6

8

10

12

14

16

0 0.005 0.01 0.015 0.02 0.025

Amphibolite

Crystalline limestone

Fragmental limestone

Taconite

Normalised Displacement (D/d)

No

rma

lise

d L

oa

d (

MP

a)

40

Table 3.4 Summary or point-load strengths and deformability [7]

Type of

material

Diameter �

(kN)

��

(MPa)

��

(mm)

���

(�� /d)

K

(m/kN)

(X l0-5)

Q

(mm) (in.)

Dolomitic

limestone

28.6 (1) 7.6 7.4 0.37 0.0131 32.5 0.74

28.6 (1) 11.1 10.7 0.43 0.0150 23.4 0.77

28.6 (1) 12.5 12.1 0.45 0.0158 22.8 0.76

50.8 (2) 38.3 11.7 0.81 0.0158 20.0 0.76

50.8 (2) 46.3 14.3 0.95 0.0196 67.3 0.61

50.8 (2) 33.7 10.3 0.70 0.0146 16.0 0.80

Fragmental

limestone

55.9 (2) 10.7 2.7 0.79 0.0141 61.6 0.71

55.9 (2) 6.7 1.7 0.51 0.0092 6.8 1.0

55.9 (2) 7.9 2.0 0.86 0.0156 9.7 1.04

Taconite 28.6 (1) 20.8 20.1 0.58 0.0170 26.8 0.75

28.6 (1) 15.6 15.1 0.53 0.0210 23.4 0.75

28.6 (1) 19.8 19.2 0.58 0.0210 18.2 0.80

Amphibolite 28.6 (1) 8.7 8.5 0.35 0.0160 28.5 0.75

26.6 (1) 8.9 8.6 0.35 0.0122 22.8 0.76

28.6 (1) 10.6 10.3 0.47 0.0133 10.8 0.98

53.9 (2) 26.8 7.3 0.76 0.0140 35.3 0.71

53.9 (2) 23.8 6.5 0.60 0.0112 16.5 0.79

53.9 (2) 24.0 6.5 0.61 0.0114 22.8 0.75

152.4 (6) 115.7 3.9 1.4 0.0092 5.4 0.87

152.4 (6) 111.2 3.8 1.09 0.0070 5.4 0.81

162.4 (6) 122.6 4.2 1.33 0.0087 10.3 0.77

152.4 (6) 121.4 4.1 0.70 0.0046 23.9 0.63

The values in Table 3.5 are larger than the 0.67 predicted by the theory of elasticity for spherical

contact. The weaker rocks (fragmental limestone and mortar) display the larger a’s or have the

more linear PDF relations. These rocks are more susceptible to local compression failure at the

points of contact. The specimen size does not appear to affect the shape of the PDF curve.

However, as can be seen in the comparison of average curves for amphibolites, Fig. 3.27, size

does affect Pnf and Dnf, The larger specimens fail at lower normalized loads or tensile stresses.

41

Table 3.5 Effect of size on average point-load strength and deformability [7]

Diameter 29mm 51.56mm Type of material

�� (kN)

�� (MPa)

� (D/d)

K (m/kN) (×10���

a �� (kN)

�� (MPa)

� (D/d)

K (m/kN) (×10���

a

Mortar 7.6 7.4 0.0124 18.5 0.84

8.6 2.6 0.0181 22.8 0.94

Amphibolite

9.4 9.1 0.0138 20.7 0.83

24.9 6.8 0.0122 24.9 0.75

Crystalline limestone

10.4 10.1 0.0146 20.2 0.76

39.4 7.3 0.0107 34.4 0.72

Fragmental limestone

10.7 8.3 0.0165 21.4 0.74

18.4 5.4 0.0130 26.0 0.92

Taconite 18.7 18.1 0.0197 22.8 0.77

33.4 11.3 0.0143 28.2 0.95

Diameter 107mm 152mm Type of material

�� (kN)

�� (MPa)

� (D/d)

K (m/kN) (×10���

a �� (kN)

�� (MPa)

� (D/d)

K (m/kN) (×10���

a

Mortar 15.3 1.32 0.011 12.3 0.76 23.3 0.71 0.014 9.7 0.72 Amphibolite

64.3 6.36 0.019 29.1 0.71 117.7

4.21 0.074 11.4 0.77

Crystalline limestone

58.4 4.52 0.017 45.2 0.70 104.4

2.34 0.096 54.2 0.70

Fragmental limestone

23.7 2.53 0.015 32.3 0.78 76. 6 1.47 0.013 35.6 0.75

Taconite 48.5 3.65 0.012 33.4 0.88 108.3

2.12 0.010 38.7 0.76

Fig.3.27. Effect of specimen size on ultimate strength and deformability.

0

2

4

6

8

10

12

0 0.005 0.01 0.015 0.02 0.025

29

54

107

152

No

rma

lise

d L

oa

d (

Mp

a)

Normalised Displacement (D/d)

3.8 Design Swing Jaw Plates

The factors of importance in designing the size of jaw crusher’s

1.3

These dimensions vary as individual manufacturers have their own specifications and

design of individual makes. In this case, we have top opening i.e. gape

bottom opening 51mm (2 in)

= 1200

= 900 mm

= 50 mm

Table

Model A B

300X400 400 300

300Χ600 600 300

300X750 750 300

300Χ900 900 300

Fig.3.28 Overall Dimensions of Typical Jaw Crusher

42

3.8 Design Swing Jaw Plates

The factors of importance in designing the size of jaw crusher’s plate

1.3

These dimensions vary as individual manufacturers have their own specifications and

In this case, we have top opening i.e. gape

1200 mm

= 900 mm

= 50 mm

Table3.6. Dimensional Chart for Jaw Crusher [6]

B C D E F

300 1050 1180 1300 700

300 1750 1680 1680 950

300 2050 1930 1850 1150

300 1850 2490 2350 1500

Overall Dimensions of Typical Jaw Crusher [32

plate are:

These dimensions vary as individual manufacturers have their own specifications and

In this case, we have top opening i.e. gape 304 mm (12 in.) and

Weight(Ton)

2.8

6.5

12

17.5

32]

43

3.9 Finite Element Analysis

3.9.1 Introduction to Finite Element Method

Development of the finite element method began in earnest in the middle to late 1950s

for airframe and structural analysis and gathered momentum at the University of Stuttgart

through the work of John Argyris and at Berkeley through the work of Ray W. Clough in the

1960s for use in civil engineering. By late 1950s, the key concepts of stiffness matrix and

element assembly existed essentially in the form used today. NASA issued a request for

proposals for the development of the finite element software NASTRAN in 1965. The method

was provided with a rigorous mathematical foundation in 1973 with the publication of Strang

and Fix's An Analysis of The Finite Element Method has since been generalized into a branch of

applied mathematics for numerical modeling of physical systems in a wide variety of

engineering disciplines, e.g., electromagnetism, thanks to Peter P. Silvester and fluid dynamics.

3.9.2 Finite Element Analysis Applications:

A variety of specializations under the umbrella of the mechanical engineering discipline

(such as aeronautical, biomechanical, and automotive industries) commonly use integrated FEM

in design and development of their products. Several modern FEM packages include specific

components such as thermal, electromagnetic, fluid, and structural working environments. FEM

allows detailed visualization of where structures bend or twist, and indicates the distribution of

stresses and displacements. FEM software provides a wide range of simulation options for

controlling the complexity of both modeling and analysis of a system. Similarly, the desired level

of accuracy required and associated computational time requirements can be managed

simultaneously to address most engineering applications. FEM allows entire designs to be

constructed, refined, and optimized before the design is manufactured.

The introduction of FEM has substantially decreased the time to take products from

concept to the production line. It is primarily through improved initial prototype designs using

FEM that testing and development have been accelerated. In summary, benefits of FEM include

increased accuracy, enhanced design and better insight into critical design parameters, virtual

prototyping, fewer hardware prototypes, a faster and less expensive design cycle, increased

productivity, and increased revenue.

44

3.9.3 Modeling using Four-Node "Tetrahedral" Element

For the realistic analysis of certain problems such as thick short beams, thick pressure

vessels, elastic half space acted on by a concentrated load and machine foundations, we have to

use three-dimensional finite elements. Just like a triangular element is a basic element for

analyzing two-dimensional problems, the tetrahedron element, with four corner nodes, is the

basic element for modeling three-dimensional problems. One of the major difficulties associated

with the use of three-dimensional elements (e.g., tetrahedral, hexahedra, and rectangular

parallelepiped elements) is that a large number of elements have to be used for obtaining

reasonably accurate results. This will result in a very large number of simultaneous equations to

be solved in static analyses. Despite this difficulty, we may not have any other choice except to

use three-dimensional elements in certain situations.

Today finite element models are often so complex that a mapped mesh with hexahedral

shaped elements is often not economically feasible. Experience shows that the most efficient and

common way is to perform the analysis using quadratic tetrahedral elements. As a consequence

of that, the total number of the degrees of freedom for a complex model increases dramatically.

Finite element models containing several millions degrees of freedom are regularly solved.

Typically iterative equation solvers are used for solving the linear equations. There are no

general rules which can be applied to decide which element shape should be preferred but there

exist some basic principles and also certain experiences from applications which can be very

helpful in avoiding simulation errors and in judging the validity of the results.

The tetrahedron element, with three translational degrees of freedom per node, is shown

in the global xyz coordinate system in Figure 3.29 (the global coordinates are denoted as x, y, z

instead of X, Y, Z, for simplicity). For this element, there will be no advantage in setting up a

local coordinate system, and hence we shall derive all the elemental equations in the global

system. Since there are 12 nodal degrees of freedom Q3i-2, Q3i-1, Q3i, Q3j-2 . . . , Q3l and three

displacement components u, v, and w, we choose the displacement variation to be linear as

1 2 3 4

5 6 7 8

9 10 11 12

( , , )

( , , )

( , , )

u x y z x y z

v x y z x y z

w x y z x y z

α α α αα α α αα α α α

= + + + = + + + = + + +

Here 1 2 12, ...α α α are constants. By using the nodal conditions

…… (3.35)

45

u=Q3i-2, v= Q3i-1, w=Q3i, at (xi, yi, zi)

u=Q3j-2, v= Q3j-1, w=Q3j, at (xj, yj, zj)

u=Q3k-2, v= Q3k-1, w=Q3k, at (xk, yk, zk)

u=Q3i-2, v= Q3i-1, w=Q3i, at (xk, yk, zk)

Fig.3.29 Tetrahedron Element in Global xyz- System

We can obtain,

3 2 3 2 3 2 3 2( , , ) ( , , ) ( , , ) ( , , ) ( , , )i i j j k k l lu x y z N x y z Q N x y z Q N x y z Q N x y z Q− − − −= + + +

Where Ni, Nj, Nk, Nl are given by Eq. (3.35).

[ ]( , , ) ( , , ) ( , , ) ( , , ) ( , , )N x y z N x y z N x y z N x y z N x y zj k l

i

=

Where

( )

( )( )

1( , , )

61

( , , )61

( , , )61

( , , )6

N x y z a b x c y d zi i i i iV

N x y z a b x c y d zj j j j jV

N x y z a b x c y d zk k k k kV

N x y z a b x c y d zl l l l lV

= + + +

= + + + = + + += + + +

…… (3.35) …… (3.36)

46

V is the volume of the tetrahedron can be obtained by following

1

1

1

1

x y zi i i

x y zj j j

Vx y z

k k kx y zl l l

=

With the other constants defined by cyclic interchange of the subscripts in the order l, i, j,

k. The sign in front of determinants in Eq. (3.38) are to be reversed when generating aj, bj, cj, dj

and al, bl, cl, dl.

1

1

1

1 1

1 1

1 1

x y z y zj j j j j

a x y z b y zi k k k i k k

x y z y zl l l l l

x z x yj j j j

c x z d x yi k k i k k

x z x yl l l l

= = −

= − = −

And similar expressions for v (x, y, z) and w (x, y, z) can also be obtained. Thus the

displacement field can expressed in matrix form as

}{ [ ] }{ 12 13 12

( , , )

( , , )

( , , )XX

u x y z

U v x y z N Q

w x y z

= =

Where

0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0

i j k l

i j k l

i j k l

N N N N

N N N N N

N N N N

=

…… (3.37)

…… (3.38)

…… (3.39)

47

And

}{

3 2

3 1

3

3

.

.

.

i

i

i

l

Q

Q

Q

Q

Q

−

−

=

Noting that all six strain components are relevant in three-dimensional analysis, the

Noting that all six strain components are relevant in three-dimensional analysis, the

strain-displacement relations can be expressed, using Eq. (11.4). as

}{ [ ] }{6 12 12 1

uxxx

vyyy

wzzz

B QX Xu vxy y x

v wyz z y

w uzxx z

ε

ε

εε ε

ε

ε

∂ ∂ ∂ ∂ ∂ ∂ = = = ∂ ∂+ ∂ ∂

∂ ∂ +∂ ∂ ∂ ∂ + ∂ ∂

[ ]

0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 01

0 0 0 06

0 0 0 0

0 0 0 0

b b b bi j k l

c c c ci j k l

d d d di j k l

Bc b c b c b c bVi i j j k k l l

d c d c d c d ci i j j k k l l

d b d b d b d bi i j j k k l l

=

The stress-strain relations, in the case of three-dimensional analysis, are given by

…… (3.40)

48

[ ] }{T Dσ ε=

Where

}Txx yy zz xy yz zx

σ σ σ σ σ σ σ=

σT is the stress tensor and

ξ is the strain displacement matrix

And [D] matrix can be defined as follows

[ ]

1 0 0 0

1 0 0 0

1 0 0 0

1 20 0 0 0 0

2(1 )(1 2 )1 2

0 0 0 0 02

1 20 0 0 0 0

2

ED

ν ν νν ν νν ν ν

ν

ν νν

ν

− − − − = + − − −

The stiffness matrix of the element (in the global system) can be obtained as

[ ] [ ][ ]( )e TK B D B dVeV

= ∫∫∫

Since the matrices [B] and [D] are independent of x, g, and z, the stiffness matrix can be

obtained by carrying out matrix multiplications as

[ ] [ ][ ]( ) ( )e e TK V B D B dV =

In this case, since the assumed displacement model is linear, the continuity of displacement along the interface between neighboring elements will be satisfied automatically.

…… (3.41)

…… (3.42)

…… (3.43)

…… (3.44)

CHAPTER -4

COMPUTATIONAL STUDY FOR SWINGING JAW PLATE AND SWINGING LEVER

49

4. COMPUTATIONAL STUDY FOR SWINGING JAW PLATE AND PITMAN

4.1 An introduction to Computer Aided Design (CAD)

Computer-aided design (CAD) is the use of computer technology for the design of

objects, real or virtual. CAD often involves more than just shapes. As in the manual drafting of

technical and engineering drawings, the output of CAD often must convey also symbolic

information such as materials, processes, dimensions, and tolerances, according to application-

specific conventions. CAD may be used to design curves and figures in two-dimensional ("2D")

space; or curves, surfaces, and solids in three-dimensional ("3D") objects. CAD is an important

industrial art extensively used in many applications, including automotive, shipbuilding, and

aerospace industries, industrial and architectural design, prosthetics, and many more. CAD is

also widely used to produce computer animation for special effects in movies, advertising and

technical manuals.

The modern ubiquity and power of computers means that even perfume bottles and

shampoo dispensers are designed using techniques unheard of by engineers of the 1960s.

Because of its enormous economic importance, CAD has been a major driving force for research

in computational geometry, computer graphics (both hardware and software), and discrete

differential geometry. Current Computer-Aided Design software packages range from 2D vector-

based drafting systems to 3D solid and surface modellers. Modern CAD packages can also

frequently allow rotations in three dimensions, allowing viewing of a designed object from any

desired angle, even from the inside looking out. CAD is used in the design of tools and

machinery and in the drafting and design of all types of buildings, from small residential types

(houses) to the largest commercial and industrial structures (hospitals and factories). CAD is

mainly used for detailed engineering of 3D models and/or 2D drawings of physical components,

but it is also used throughout the engineering process from conceptual design and layout of

products, through strength and dynamic analysis of assemblies to definition of manufacturing

methods of components. It can also be used to design objects. Design is an activity that facilitates

the realization of new products and processes through which technology satisfies the needs and

aspirations of the society. Engineering design of a product may be conceived and evolved in four

steps:

50

1. Problem definition: Extracting a coherent appreciation of need or function of an engineering

part from a fuzzy mix of facts and myths that result from an initial ill-posed problem. The data

collection can be done via observation and/or a detailed survey.

2. Creative process: Synthesizing form, a design solution to satisfy the need. Multiple solutions

may result (and are sought) as the creative thought process is aided by the designers’ vast

experience and knowledge base. Brainstorming is usually done in groups to arrive at various

forms which are then evaluated and selected into a set of a few workable solutions.

3. Analytical process: Sizing the components of the designed forms. Requisite functionality,

strength and reliability analysis, feasible manufacturing, cost determination and environmental

impact may be some design goals that could be improved optimally by altering the components’

dimensions and/or material. This is an iterative process requiring design changes if the analysis

shows inadequacy, or scope for further improvement of a particular design. Multiple solutions

may be evaluated simultaneously or separately and the best design satisfying most or all

functional needs may be chosen.

4. Prototype development and testing: Providing the ultimate check through physical

evaluation under, say, an actual loading condition before the design goes for production. Design

changes are needed in the step above in case the prototype fails to satisfy a set of needs in step 1.

This stage forms an interface between design and manufacture. Many groups encourage

prototype failure as many times as possible to quickly arrive at a successful design.

4.1.1 An Introduction to CATIA:

CATIA (Computer Aided Three-dimensional Interactive Application) is a multi-platform

CAD/CAM/CAE commercial software suite developed by the French company Dassault

Systems and marketed worldwide by IBM. Written in the C++ programming language, CATIA

is the cornerstone of the Dassault Systems product lifecycle management software suite. The

software was created in the late 1970s and early 1980s to develop Dassault's Mirage fighter jet,

and then was adopted in the aerospace, automotive, shipbuilding, and other industries. CATIA

competes in the CAD/CAM/CAE market with Siemens NX, Pro/ENGINEER, Autodesk Inventor

and Solid Edge.

51

4.1.2 Solid Modeling of Swing Jaw Plate and Pitman using CATIA

Engineering components can be of various forms (sizes and shapes) in three-dimensions. A

Solid can be thought of as composed of a simple closed connected surface that encloses a finite

volume. The closed surface may be conceived as an interweaved arrangement of constituent

surface patches, which in turn, can be individually considered as composed of a group of curves.

It then behooves to discuss the generic design of curves, surfaces and solids in that order. Even

before, it may be essential to understand how three-dimensional objects or geometrical entities

are represented on a two-dimensional display screen, and how such entities can be positioned

with respect to each other for assembly purposes or construction operations. Engineers have

converged to numerous standard ways of perceiving a three-dimensional component by way of

engineering drawings depicted on a two-dimensional plane (conventionally blue prints, but for

CAD’s purpose, a display screen).

The Sketcher workbench is the basic 3D wireframe elements. In addition to the reference

features and geometry creation, it is having sketch operations, constraints, and dimensions. The

CATIA Part Design workbench is the modeling techniques used to create and edit designs and

feature-based solids are explored. It includes sketch-based features, dress up features, and

patterns. CATIA Assembly Design workbench describes the methods of building assemblies of

the various parts of the system or structure. It also includes the assembly information, operations,

tools, catalogs, analysis, parameters, formulas, and interpart links.

3D modeling of swinging jaw plate and swinging lever includes under the part design

module and the tools required to model these include pads, pockets, holes, drafts, fillets,

chamfers, threads, patterns, and mirror. Once modeling is complete it is needed to be assembled

pitman with swinging jaw plate with the help of contact constraints and surface constraints.

Fig.4.1 to Fig.4.4 shows the 3D modeling of swinging jaw plates with no stiffeners, one stiffener,

two stiffeners, and three stiffeners, and Fig.4.5 represents the conventional pitman or swinging

lever.

Dimensions of the swinging jaw plate:

I. Thickness = 140mm.

II. Length = 1200mm.

III. Width = 900mm.

Dimensions of the stiffener attached to the jaw plate:

I. Length= width of the jaw plate= 900mm

II. Width of the stiffener = 100mm

III. Height of the stiffener = 75mm

52

Once modeling of the swinging jaw plate and pitman of the single toggle jaw crusher

completed next step is to assemble or fastening the jaw plate to the pitman by using proper

surface constraints. Fig.4.6 represents the assembled structure of the swinging jaw plate with

pitman.

Fig.4.1 Swinging jaw plate without stiffeners

Fig.4.2 Swinging jaw plate

with one stiffener

Fig.4.3 swinging jaw plate with two stiffeners

Fig.4.4 swinging jaw plate

with three stiffeners

Fig.4.5 swinging lever of the

single toggle jaw crusher

Fig.4.6 assembled structure of

swinging jaw plate with pitman

53

4.2 Computer Aided Analysis

Machine elements are required to operate in environmental conditions where they may be

subjected to forces, extreme thermal conditions, and unfavorable weather conditions and so on.

The element must be designed to withstand the harmful effects of the environment and to operate

satisfactorily. Hence, the designer must formulate a mathematical model for the element;

represent the behavior or the response of the element. There are several methods available to

solve the resulting differential equations describing the behavior of the element or the system, of

which the element is a part. Finite difference methods, transfer matrix methods, finite element

methods are some of typical methods that can be used for the mathematical representation of the

system and direct numerical integration or modal analysis techniques are some possible analysis

techniques to obtain the system response when subjected to environmental excitations.

When the element being designed is quite complex or when the element behavior can be

understood only by analyzing the complete system. Computers can be very efficiently used for

the routine and repetitive computations involved in all these analysis methods.

4.2.1 Generative Structural Analysis in CatiaV5:

Structural analysis of a component is very important process for design and development

of any part. It enables a designer and engineer to check if the design can take the required loads,

if the material is good enough for the stresses, critical sections within the design and lots more.

Generative Structural Analysis (GSA) is used for Finite Element Analysis of 3D parts. GSA

allows the user to quickly model a part’s mechanical behavior with very few steps. GSA

provides verity of tools and stress visualization options.

4.3Finite Element Analysis:

Using CATIA V5 the overall process for FEA can be subdivided into smaller steps

shown in Fig.4.7. These steps are explained below.

4.3.1 Pre-Processing

This will involve the complex physical structure to be converted into an equivalent Finite

Element model. This will be followed by applying the material properties to the model. There are

five structural properties, Young’s Modulus, Poisson Ratio, Density, Thermal Expansion and

Yield Strength. Next step within pre-processing applying the boundary conditions and restraining

to the FE model. And finally conversion of actual loads to equivalent FE Loads.

54

4.3.2 Computation

In computation step the standard FE solutions procedures uses data provided by pre-

processing step and then solves the FE model to find out the unknown displacement values.

4.3.3 Post-Processing

Using the values of displacement computed in

pervious step strain and stresses are calculated for the whole

structure. The deformation of the structure can be studied by

looking at the variation of strains and stresses throughout the

structure.

4.3.4 Mesh Refinement Iteration

In order to get a more accurate solution, the mesh

needs to be refined and the computation is to be done. A

number of mesh refinement and computations iterations are performed till the required solution

accuracy is achieved.

4.3.5 Report Generation

Once the required accuracy level is achieved, various plots such as Displacement,

Principal stress, Von-Mises Stress can be obtained.

4.4 Static Stress Analysis of Assembled Structure Using CATIA

4.4.1 Assumptions

A static analysis calculates the effects of steady loading conditions on a structure, while

ignoring inertia and damping effects, such as those caused by time-varying loads. To simulate

the stress behavior of corrugated jaw plate some assumptions and approximations are required.

Here analysis was undertaken based on the assumption that the point load strength of the disk

and irregularly shaped particles to be equal and tensile point loads of different particle sizes are

acting normal to the plate.

Fig.4.7 Finite Element

Analysis Process

55

4.4.2 Applying material:

Before the Generative Structural Analysis module used for the FEA of assembled

structure, it must have material assigned to it. Each material in CATIA V5 has mechanical

properties for computing the analysis. These properties are Young’s Modulus, Poisson Ratio,

Density, Thermal Expansion and Yield Strength. Material properties of the swinging jaw plate

and pitman are shown in Table.4.1.

Structure Material used Youngs

modulus(GPa)

Yield

strength(MPa)

Poisions

ratio

Density

(Kg/m3)

Swinging

jaw plate

Martensitic steel

(C-1.1%, Mn-13%) 210 550 0.266 7860

Pitman

Austenite steel

(C-0.04%, Mn-0.7%, Cr-

13%, Ni-4%,Mo-0.8% )

200 300 0.266 7860

Table.4.1 Material properties of swinging jaw plate & pitman

4.4.3 Assembling of Swinging Jaw Plate and Pitman

When create a connection, generally first create an assembly constraint in the Assembly

Design workbench. Then, add a property in the Generative Structural Analysis workbench, on

this constraint (fastened, pressure fitting, bolt and so forth). This property generates a Mesh part.

Fig.4.8 Assembly constraints applied to jaw plate and pitman

56

Property connections are assembly connections used to specify the boundary interaction

between bodies in an assembled system.

Creating Fastened Connections: Fastens bodies together at their common interface.

Creating Slider Connections: Fastens bodies together at their common interface in the normal

direction while allowing them to slide relative to each other in the tangential directions.

Creating Contact Connections: Prevents bodies from penetrating each other at a common

interface.

Creating Pressure Fitting Connections: Prevents bodies from penetrating each other at a

common interface.

Creating Bolt Tightening Connections: Prevents bodies from penetrating each other at a

common interface.

Creating Virtual Rigid Bolt Tightening Connections: Takes into account pre-tension in a bolt-

tightened assembly in which the bolt is not included.

Creating Rigid Connections: Fastens bodies together at a common rigid interface.

Creating Smooth Connections: Fastens bodies together at a common soft interface.

Creating Spot Welding Connections: Fastens bodies together at a common soft interface.

4.4.4 Fastened connections:

A Fastened Connection is the link between two bodies which are fastened together at

their common boundary, and will behave as if they were a single body. From a finite element

model viewpoint, this is equivalent to the situation where the corresponding nodes of two

compatible meshes are merged together. However, since bodies can be meshed independently,

the Fastened Connection is designed to handle incompatible meshes.

The Fastened Connection relations take into account the elastic deformability of the

interfaces.

The program proceeds as follows:

1. Each node of the finer surface mesh is projected parallel to the local outer normal of the

first surface onto the second surface mesh.

2. A projection point is located whenever possible at the intercept of the projection direction

with the second surface mesh (at the face boundary by roughly half an element width).

3. If a projection point exists, the start node is connected by a kinematical spider element to

all nodes of the element face on which the projection point has landed.

57

4. A set of join-type relations is computed between the start node degree of freedom and the

connected nodes degree of freedom.

Thus, the Fastened Connection generates at most as many spider kinematical elements as

there are nodes on the finer surface mesh for which a projection onto the opposite surface mesh

exists.

4.5 Linear Static Stress Analysis:

The analysis for the swinging jaw plate with pitman has been conducted to obtain Von

Misses stresses and deformation in the structure.

1. The objective of the work is to minimize the Von Misses stresses and deformation developed

during the crushing.

2. Reduce the weight of the swinging jaw plate by attaching stiffeners to the jaw plate along its

width.

4.5.1 Applying Boundary Conditions

Since one end of the pitman is hinged to the eccentric shaft and other end is connected is

to the toggle plate. Fig4.10 represents the boundary conditions applied to the assembled

structure.

Fig.4.9 Property on the constraint Fig.4.10 Boundary conditions to the pitman

58

Optimization of toggle plate width & location:

While the material is nipping in the crushing chamber toggle supports the swinging lever

at bottom end it means toggle plate is more affected during the crushing. So it is necessary to

optimize the toggle plate dimensions and location of the toggle plate along the pitman.

4.5.2 Analysis for Optimizing the Toggle Plate Width:

Analysis is performed for assembled structure of swinging jaw plate with swinging lever

for a conventional single toggle jaw crusher with constant toggle plate thickness and length. And

the width of the toggle plate is considered at 100, 200, 400, 600, 800, 900mm. It is observed that

as the width of the toggle plate increases Von Misses stress as well as displacements in the

structure decreases. Table4.2 represents how the Von Misses stresses and displacements are

varying with toggle width.

Fig.4.11 Toggle Plate of the jaw crusher

Width of the Toggle Plate(mm) 100 200 400 600 800 900

Von Misses Stress(N/mm2) 447 246 188 137 98.6 97.7

Displacement (mm) 0.311 0.262 0.212 0.18 0.164 0.16

Table.4.2 Von Misses stress and displacements at various sizes of the Toggle Plate widths.

By observing graph shown in Fig.4.12 between Von Misses stress and toggle plate width

at the width of 800mm, the curve reaches to an asymptotic value of 98.6 N/mm2. The

displacement curve for various toggle plate width is shown in Fig.4.13. So the optimal value of

the toggle plate width can be taken as 800mm and the Von Misses stress and displacement are

98.6N/mm2 and 0.164mm respectively.

Fig.4.12 Vonmisses stresses vs toggle plate width

Fig.4.14 to Fig.4.19 represents the Von Misses stress and displacement of the assembled

strcture when the width of the

Fig.4.14 Von Misses Stress and Displacements for the Toggle plate width

0

50

100

150

200

250

300

350

400

450

500

100 200 400

N/m

m2

N/m

m2

mmmm

59

be taken as 800mm and the Von Misses stress and displacement are

and 0.164mm respectively.

stresses vs toggle plate width Fig.4.13 displacements vs toggle plate

width

Fig.4.14 to Fig.4.19 represents the Von Misses stress and displacement of the assembled

the width of the toggle plate is considered at 100, 200, 400, 600, 800, 900mm.

Von Misses Stress and Displacements for the Toggle plate width

600 800 900

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

100 200 400

be taken as 800mm and the Von Misses stress and displacement are

displacements vs toggle plate

Fig.4.14 to Fig.4.19 represents the Von Misses stress and displacement of the assembled

is considered at 100, 200, 400, 600, 800, 900mm.

Von Misses Stress and Displacements for the Toggle plate width of 100mm

600 800 900

mm

60

Fig.4.15 Von Misses Stress and Displacement for the Toggle plate width of 200mm

Fig.4.16 Von Misses Stress and Displacement for the Toggle plate width of 400mm

61

Fig.4.17 Von Misses Stress and Displacement for the Toggle plate width of 600mm

Fig.4.18 Von Misses Stress and Displacement for the Toggle plate width of 800mm

62

Fig.4.19 Von Misses Stress and Displacement for the Toggle plate width of 900mm or

throughout the width of the swinging jaw plate.

4.5.3 Anlysis for Optmizing the Toggle Plate Location:

Analysis has been performed ,locating the toggle plate at position of 0, 50, 100, 150, 200,

250, 300mm form bottom surface of the pitman. Fig.4.20 & Fig.4.21 shows the VonMisses stress

and deformation of the strcture when toggle plate is located at different positions. It is observed

that the Von Misses stress are first decreasing upto the locating length is 100mm, again

increasing upot 150mm and decreasing at the leangth of 200mm, further increasing the location

length from pitman bottom surface Von Misses stresses are increasing.

Fig.4.20 Von Misses stress vs toggle location Fig.4.21 displacement vs toggle location

0

20

40

60

80

100

120

0 100 200 300 400mm

N/m

m2

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

0 100 200 300 400mm

mm

63

In Fig.4.21, it is observed that the deformation is decreasing up to the location length of

100mm, and then increasing. By the obtained results the optimal location of the toggle plate is

100mm form the bottom face of the pitman. Fig.4.22 to Fig.4.27 represents the Von Misses

stresses and the deformation of the structure, toggle plate is locating at various positions

.

Fig.4.22 Von Misses Stress and Displacement ,Toggle plate located at bottom

Fig.4.23 Von Misses Stress and Displacement ,Toggle plate located at 50mm from bottom

64

Fig.4.24 Von Misses Stress and Displacement ,Toggle plate located at 100mm from bottom

Fig.4.25 Von Misses Stress and Displacement ,Toggle plate located at 150mm from bottom

65

Fig.4.26 Von Misses Stress and Displacement ,Toggle plate located at 200mm from bottom

Fig.4.27 Von Misses Stress and Displacement ,Toggle plate located at 250mm from bottom

66

4.5.4 Analysis by considering stiffeners to the swinging jaw plate :

Many engineering structures consist of stiffened thin plate and shell elements to improve

the strength to weight ratio. This analysis has performed attaching one stiffener, two stiffeners,

and three stiffeners to the 140mm thick swinging jaw plate. During this analysis width of the

toggle plate is considered as 800mm and toggle is located at 100mm from the bottom face of the

pitman. Fig.4.29 to Fig.4.31 shows the Von Misses stress and deformation of the structure when

considering one stiffener, two stiffeners and three stiffeners.

Fig.4.28 represents the assemble system of jaw plate and pitman with one stiffener, two

stiffeners, three stiffeners.

Fig.4.28 swinging jaw plate with one stiffener, two stiffeners, three stiffeners

Table.4.3 represents the Von Misses stress and displacements ,when stiffeners attached to

the swinging jaw plate.

Number of stiffeners Von Misses stress

(N/mm2)

Displacement(deformation)

(mm)

1 158 0.836

2 68.3 0.145

3 53.9 0.0883

Table.4.3 Von Misses stress and displacement, swinging jaw plate with stiffeners.

67

Fig.4.29 Von Misses Stress and Displacement ,using single stiffener

Fig.4.30 Von Misses Stress and Displacement ,using two stiffeners

Fig.4.31 Von Misses Stress and Displacement ,using two stiffeners

68

4.6. Validation of Results:

Obtained results from finite element analysis have been compared with existing design

methodology for swinging jaw plate of a single toggle jaw crusher developed by Chrlesh H.

Dowding [7]. He considered swinging jaw plate as abeam model was loaded with the particles

which were all assumed to fail simultaneously.

Table.4.4 represents the comparison of results for deformations produced by Chrlesh H.

Dowding model and present model, without considering stiffeners.

Thickness of the plate

(mm)

Deformation by

Chrlesh H. Dowding

(mm)

Deformation by

Present model

(mm)

% of Error

140 0.292 0.311 6.1%

152 0.226 0.238 5.04%

Table.4.4 Comparison of results with Chrlesh H. Dowding results.

CHAPTER -5

RESULTS, DISCUSSION AND CONCLUSION

69

5. RESULTS, DISCUSSION AND CONCLUSIONS

5.1 Force Distribution along the Swinging Jaw Plate:

The distribution of the forces along the liner can be calculated by the product of mass of

the swinging jaw plate and the resultant acceleration produced by the jaw plate at various points

on the liner.

F= 2 2

u vM a a+ 2 2

u vM a a= +

Where ax=horizontal acceleration & ay=vertical acceleration.

au= acceleration in U- direction & av= acceleration in V direction.

By rotating the eccentric shaft (crank) of complete cycle the distribution of forces on the

liner of the swinging jaw plate variations are shown. By this the forces are more fluctuating at

the end of the swinging jaw plate and the fluctuations are decreasing when the distance is

increasing from the lower point , finally it approximates to a straight line as shown in the Fig.5.1.

Resultant accelerations for x and y directions and u and v directions are shown in Fig.5.1 and

Fig.5.2.

Fig.5.1 Force distribution on the swinging jaw plate considering X and Y direction accelerations

0.0E+00

4.0E+03

8.0E+03

1.2E+04

1.6E+04

2.0E+04

0 120 240 360

mm

/s2

Ф(Degrees)

1

2

3

4

5

6

7

8

9

10

11

70

Fig.5.2 Force distribution on the swinging jaw plate considering U and V direction accelerations

5.2 Wear Analysis:

Jaw plates wear is determined by the close process. Two key factors in this process

affecting the jaw plates wear are squeezing and sliding. At present, the high manganese steel is

widely used as the jaw plate material, which has the outstanding work hardening character. By

scanning the worn jaw plates, it is found that the sliding is the main factor to the jaw plates wear

and the sufficient squeezing can even relieve the jaw plate wear.

Now, some of the phenomenon in practice can be explained. Since the sliding is small at

the inlet part of the chamber and the squeezing plays the main role, the wear in this zone is small.

With the horizontal stroke decreasing and the vertical distance increasing, the wear becomes

more and more serious. Because fewer particles are crushed in the edge parts, the wear of the

middle part in the same crushing zone is much serious comparing with the edge parts.

For the same jaw crusher, the slide between the particle and the fixed jaw plate is more

than that between the particle and the moving jaw plate, so the wear of the fixed jaw plate is

more serious relative to the moving jaw plate wear.

0.0E+00

4.0E+03

8.0E+03

1.2E+04

1.6E+04

2.0E+04

0 120 240 360

mm

/s2

Ф(Degrees)

1

2

3

4

5

6

7

8

9

10

11

71

5.3 Optimization of Width and Location of Toggle Plate:

While the material is nipping in the crushing chamber toggle supports the swinging lever

at bottom end it means toggle plate is more affected during the crushing. So it is necessary to

optimize the toggle plate dimensions and location of the toggle plate along the pitman.

By performing finite element analysis on the assembled system of swinging jaw plate and

pitman for a typical PE 300x900 series type jaw crusher, it is found that the optimal value of the

toggle width is 800mm at which the Von Misses stresses are approaching to asymptotic value at

98.6 N/mm2 as shown in the Fig. and the deformation is 0.164mm.

For a conventional PE 300x900 series type jaw crusher, toggle plate is located

approximately at 300mm from the bottom of the pitman. But analysis gives the optimal value of

toggle plate location is 100mm above form the bottom of the pitman and the Von Misses and

deformation obtained are 54N/mm2 and 0.0765mm.

5.4 Optimization of Mass of the Swinging Jaw Plate:

Using stiffeners, strength to weight ratio of the jaw plate can be increased. Analysis has

been performed on the assembled structure when swinging jaw plate is having without stiffener,

one stiffener, two stiffeners and three stiffeners. Fig.5.3 to Fig.5.5 represents the mass of the

stiffened jaw plates. The Von Misses and deformation are tabulated in the Table.5.1

Fig.5.3 Mass of one stiffener jaw plate

72

Fig.5.4 Mass of two stiffeners jaw plate

Fig.5.5 Mass of three stiffeners jaw plate

73

No of stiffeners Von Misses stress

(N/mm2)

Deformation

(mm)

Mass of the jaw plate

(kg)

0 54 0.0765 1018.314

1 158 0.836 701.882

2 68.3 0.145 739.683

3 53.9 0.0883 776.683

Table.5.1 Von Misses stress, Deformation and Mass of the jaw plate with stiffeners

Table.5.1 shows that the Von Misses stresses and deformation of the swinging jaw plate

without stiffeners are approximated to the jaw plate having three stiffeners. Therefore mass

reduction of the jaw plate during the usage of stiffeners is

% of mass reduced= (mass of jaw plate without stiffeners- mass of jaw plate with three

stiffeners) *100/ mass of jaw plate without stiffeners

= (1081.314-776.683)*100/1018.314

= 23.73%

74

5.5 Conclusion

1. A certain domain of the coupler plane and some points are chosen on the crushing interface

or the liner. Based on the computation and the analysis of the practical kinematic

characteristic of the points along the liner domain, some traditional motion parameters are

calculated. According to the requirement for the squeezing motion of different zone in the

crushing chamber, the chamber geometry can be improved.

2. The movement of the moving jaw crusher is described in detail. The force distribution is

analyzed with the different operational parameters, so the distribution feature of the force on

the liner is obtained. The job is helpful for a design of new prototype of this kind of machine

on optimizing the frame, designing the chamber and recognizing the crushing character.

3. Results obtained from the movement analyses of the moving jaw and the crushing force

distribution analysis, the jaw plates wear is analyzed. The relationship between the slide and

the wear is reasonable and some results of the wear analysis are validated in practice.

Predicting the jaw plates wear on a macroscopic level will be helpful to the jaw crusher

design for better performance.

4. Finite element analysis of swing jaw plates is carried out, using four - noded tetrahedral

element to predict the optimized width and the location of the toggle plate, when it is

subjected to point loading under simply supported boundary conditions.

5. The stiffened plate models which leads to reductions in plate weight and indicates that design

of new energy-efficient systems of the crushed material.

6. In case stiffened jaw plates as the number of stiffener increases the strength/weight ratio of

the jaw plate increases making it stronger than that of without stiffener.

7. The stiffened plate models which leads to 25% saving in energy, of course this 25% is an

estimate for a typical 600*900 series jaw crusher.

8. Rock strength has only been of interest because of the need to know the maximum force

exerted by the toggle for energy considerations. Thus a swing plate, stiff enough to crush

taconite, may be overdesigned for crushing a softer fragmental limestone.

75

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