“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 Rourkela
CERTIFICATE This is to certify that the thesis entitled, “Optimum Design and Analysis of Swinging Jaw Plate of a Single Toggle Jaw Crusher” Crusher submitted by Mr. B B V L Deepak in partial fulfillment of the requirements for the award of Master of Technology Degree in Mechanical Engineering 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 and 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:
Dr. N. Kavi Department of Mechanical Engineering National Institute of Technology Rourkela-769008 Rourkela
CONTENTS Title Abstract
Page No. 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 4.2.1 Generative Structural Analysis in CatiaV5 4.3 Finite Element Analysis
53 53 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
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.
i
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 ii
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
iii
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 iv
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 v
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
vi
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
vii
CHAPTER-1
INTRODUCTION AND SCOPE FOR STUDY
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. 1
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]
2
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]
3
(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]
4
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 5
tremendous
force
to
each
stroke.
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.
6
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 7
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. 8
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 make the moving jaw approach and leave the fixed jaw periodically with respect to eccentric shaft rotation,, 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 as the desired dimension of the crushed product. A fixed jaw mounted in a “V” alignment is the stationary breaking surface while while the movable jaw exerts force on the rock by forcing it against 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 into smaller sizes and slip down in the crushing chamber. chamber. In the return stroke, further reduction of size is 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 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 of the moving jaws, heavy flywheels are used in both types of crushers mounted on each side of the eccentric shaft. 9
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
Average
Min
Max
Toggle Speed, rpm Min Max
Min Max Min Max 125 1600 150 2100 4:1/9:1
7:1
2.25
225
100
300
125 1600
150
7:1
2.25
400
120
300
100
150
7:1
2.25
11
250
300
Gape, mm
Blake double toggle Blake single toggle Dodge Type
Reduction Ratio
280
Width, mm
Range
2100 4:1/9:1
28
4:1/9:1
Power, kW
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. 10
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.
11
CHAPTER -2
LITERATURE REVIEW
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 12
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 13
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 pointloading 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.
14
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 pointloaded 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
15
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 16
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.
17
CHAPTER -3
THEORETICAL ANALYSIS AND DATA COLLECTION
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 18
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.
19
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 4bar 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.
20
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. 21
The dimensions defined by those particle sizes are (Fig.3.2 (Fig ): 1.The gape - the distance between the jaws at the feed opening 2.The The closed side set (CSS) - the minimum opening between the jaws during the crushing cycle (minimum discharge aperture) 3.The The open side set (OSS) – the maximum discharge aperture 4.The throw – the stroke of the swing jaw and the difference between OSS and CSS.
Fig.3.2 Jaw Crusher sketch(12)
3.3 Choosing the Points along the Liner for Computing: A liner of jaw crusher is an interface for analyzing the crushing ng force, on which the crushing force 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 crusher. The liner is one of the curves in the cross-section section of the couple plane, which is also given a definition as one of the coupler curves in a fourbar crank-rocker rocker model. Since different positions of liners in the coupler plane have different moving features, the motion of points along the liners ners in the computing domain is quite different from that of them in the straight-line straight coupler of the simple fourbar crank-rocker crank 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. Based on the fourbar crank-rocker crank model, the system sketch of jaw crusher for fo calculating is shown in Fig.3.3. 3.3. The global static coordinate is XOY and the dynamic coordinate is UCV. Although a real shape and position of a fixed working liner is usually determined by a 22
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. 900 750 600
y(mm)
450 300 150 0 -150 -300 0
150 300 450 x(mm)
Fig.3.3 Points track along the liner
23
3.4 Movement Computation and Feature Analysis of Points: The mechanism of thee jaw crusher is shown in Fig.3.2; ggiven iven the rotation direction of the crank AB is clockwise.
= Crank angle made by vertical Where ∅= θ= Angle between een two plates ≤ 900 and sin θ =
−mn + (mn) − (n + 1)(m − 1) n +1 2
2
2
2
cos θ = m + n sin θ
………………
(3.1)
………………
(3.2)
m=
a + b + r + l − k − 2r (a sin φ + b cos φ ) n +1
n=
a − r sin φ b − r cos φ
2
2
2
2
2
2
…………… (3.3)
……………..
(3.4)
By rotating crank (∅) from 00-3600 the variation of nip angle (θ)) is shown in Table 3.2. 0
36
72
108
144
180
216
252
18.898
19.473
19.994
20.249
20.146
19.742
19.192
18.696
288
324
360
18.43
18.501
18.898
Table 3.2: variation of nip angle with crank angle Given the position of any point in dynamic coordinate UCV is (u, v) and in global coordinate XOY is (x, y) as shown in Fig. Fig.3.4. As mentioned above B C = l , AB = r . By observing Fig.
AK = r sin(90 − φ) , BK = r cos(90 − φ ) .
And
LP ' = u cos θ , PP ' = u sin θ , M N = a − BK
= a − r sin φ NL = (BC − LC)sinθ = (l − v)sin θ
Fig.3.4 Point consideration in dynamic coordinate 24
AP = AK + K ' P K ' P = BN − PP '
⇒ AP = AK + BN − PP '
⇒ AP = r cos φ + (l − v)cosθ − u sin θ Therefore horizontal displacement: x = M N + N L + LP '
∴ x = a − r sin φ + (l − v)sinθ + u cosθ
………………
(3.5)
And vertical displacement:
y = b − AP ∴ y = b − r cosφ − (l − v)cosθ + u sinθ
………………..
(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. 450
900 1
400
1
350
2
2
700
3
3
4
500
4
5
5
250
mm
x(mm)
300
6 200
300
6 7
7 8
150
100
8
9
100
9
10 50
-100
10
11
0
11 -300
0
120
240
360
0
Ф(Degrees)
120
240
360
Ф(degrees)
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. 25
320
310
228
310
300
mm
232
mm
y(mm)
320
300
224
290
220
290
280
216
280 0
215 220x(mm) 225 230 235
Fig.3.7 6th Point Track
120 240 Ф(Degrees)
0
360
Fig.3.8 6th Point horizontal Displacement
120 240 Ф(Degrees)
360
Fig.3.9 6th Point Vertical Displacement
And the velocity of the points can be express as following equations:
dθ r (a + l sin θ )cos φ + (l cos θ − b)sin φ = ……………… (3.7) dφ l a − r sin φ + (b − r cos φ ) Velocity in X-direction (VX) can be expressed with respect to crank rotation as
Since
vX =
dx dt
dx dφ = dφ dt
d = ( u cosθ + (l − v)sin θ + a − r sin φ ) ω dφ dθ dθ − r cos φ − u sin θ ω v = (l − v)cosθ dφ dφ X
……………… (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. 1
450
2
vx mm/s
300
3 4
150
5
0
6
-150
7 8
-300
9
-450
10
0
120 240 Ф(Degrees)
360
Fig.3.10 Horizontal velocities 26
11
And velocity in Y-direction (Vy) can be expressed with respect to crank rotation as vX =
dx dx dφ = dt dφ dt
d = ( u cos θ + (l − v)sin θ + a − r sin φ ) ω dφ
dθ dθ vY = (l − v)sin θ + r sin φ + u sin θ ω dφ dφ
……………… (3.9)
The vertical velocity variation for 11 points along the liner or swinging jaw plate
vy mm/s
relative to the angle parameter Ф is shown in Fig.3.11. 600
1
400
2
200
3 4
0
5
-200
6
-400
7 8
-600 0
120
240
360
Ф(Degrees)
9 10 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.
dθ v = (l − v) − r cos(φ + θ ) ω dφ
………………
(3.10)
dθ v = u + r sin(φ + θ ) ω dφ
………………
(3.11)
U
V
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 27
variation is minimal for the points at the suspending point zone. The variation of the initial phase has a certain law. 600 400 vu mm/s
200 0
-200 -400 -600 0
120 240 Ф(Degrees)
360
1 2 3 4 5 6 7 8 9 10 11
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. 450 300 mm/s
150 0 -150 -300 -450 0
120
240
Ф(Degrees)
360
1 2 3 4 5 6 7 8 9 10 11
Fig.3.13 V-directional Velocities Therefore the accelerations along the X direction (ax) and Y direction (ay) can also be found as follows.
aX =
dvX dvX dφ = dt dφ dt 28
=
d dθ dθ 2 − r cos φ − u sin θ (l − v) cos θ ω dφ dφ dφ
2 d 2θ dθ 2 ∴ a = [ (l − v ) cos θ − u sin θ ] − [ (l − v) sin θ + u cos θ ] + r sin φ ω 2 x dφ dφ ….. (3.12)
aY =
=
dvY dvY dφ = dt dφ dt d dθ dθ 2 + r sin φ + u sin θ (l − v)sin θ ω dφ dφ dφ
2θ dθ 2 d 2 ∴ a = [ (l − v ) s inθ + uco s θ ] + [ (l − v )co s θ − u sin θ ] + rco s φ ω 2 y dφ dφ ….. (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
1.5E+04
1
2.0E+04
1
1.0E+04
2
1.5E+04
2
3
1.0E+04
3
4
5.0E+03
4
0.0E+00
5
-5.0E+03
6
7
-1.0E+04
7
8
-1.5E+04
8
9
-2.0E+04
9
5.0E+03 0.0E+00
5
-5.0E+03
6
-1.0E+04 -1.5E+04 0
120
240
360
Ф(Degrees)
ay mm/s2
ax mm/s2
the crank angle∅ varying from 00- 3600.
0
10 11
120
240
Ф(Degrees)
Fig.3.14 Horizontal accelerations
360
10 11
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∅. 29
aU =
=
dvU dvU d φ = dt d φ dt
d dθ dθ 2 + r sin φ + u sin θ (l − v)sin θ ω dφ dφ dφ
dθ 2 d 2θ ∴ aU = (l − v ) + r sin(θ + φ ) 1 + ω φ dφ d
And
aV =
=
……………… (3.14)
dvV dvV dφ = dt dφ dt
d dθ + r sin(θ + φ ) ω 2 u dφ d φ
d 2θ dθ ∴ aV = u + rco s(θ + φ ) 1 + ω 2 dφ dφ 1.5E+04 1.0E+04
……………… (3.15)
1
1.5E+04
2
1.0E+04
5.0E+03
5.0E+03
4
0.0E+00
5
-5.0E+03
6
mm/s2
au mm/s2
3
-5.0E+03
7 -1.0E+04
8
-1.5E+04
0.0E+00
-1.0E+04
9
0
60 120 180 240 300 360 Ф(Degrees)
10 11
Fig.3.16 U-directional accelerations
-1.5E+04 0
120 240 Ф(Degrees)
360
Fig.3.17 V-directional accelerations
30
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.
31
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 32
Considering equilibrium for Fig (a) Equilibrium in horizontal direction: N1 sin α − f1 cos α − N 2 = 0
………
(3.16)
………
(3.17)
Equilibrium in vertical direction: N1co s α + f1 sin α − f 2 = 0
⇒ N1co s α + µ N1 sin α − µ ' N 2 = 0
………
(3.18)
Given that the slide first takes place between the particle and the moving jaw plate. The friction coefficient isµ. ⇒ f1 = µ N1
………
(3.19)
The friction coefficient between the particle and the fixed jaw plate will be µ’ ⇒ f2 = µ ' N 2
………
(3.20)
………
(3.21)
⇒ N 2 = N1 ( sin α − µ cos α ) ………
(3.22)
By equations (3.16) & (3.19) N1 sin α − µ N1 cos α − N 2 = 0
From equation (3.18)
µ'=
( co s α + µ sin α ) > 0 ( sin α − µ cos α )
⇒ µ −µ'= µ − =
(3.23)
………
( co s α + µ sin α ) ( sin α − µ cos α )
− µ 2 cos α − cos α <0 sin α − µ cos α
..…… (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) ⇒ f2 = µ N2 The friction coefficient between the particle and the moving jaw plate will be µ’.
⇒ f1 = µ ' N1
……. (3.27)
Form equation (3.16) & (3.27)
N 2 = N1 ( sin α − µ 'cos α )
……. (3.28)
33
Form equation (3.17) & (3.26) ⇒ N1 (co s α + µ 'sin α ) − µ N 2 = 0
……. (3.29)
∴ The friction coefficient between the particle and the moving jaw plateµ’ can be found from equations (3.28) & (3.29)
( −co s α + µ sin α ) ( sin α + µ cos α ) ( −co s α + µ sin α ) µ−µ'= µ− ( sin α + µ cos α ) µ'=
And
=
µ 2 cos α + µ cos α >0 sin α + µ cos α
…… (3.30)
……. (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] 34
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.
A
B
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. 35
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. 36
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.
Cylinder Particle Irregular Particle Sphere Particle Fig.3.25. Comparison of plate and point-loaded particles. 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 pointloading 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). P=
St d 2 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 37
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:
9 P2 (1- n 2 ) D = 2 . 2 16 RE r
1/3
………..
(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
D=1.6
P2/3 R1/3E2/3 r
………..
(3.33)
Therefore any given sphere will deform according to a deformation hardening power law: D=KP a
………..
(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: sandcement 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] E (MPa)
q (Mpa)
Location
Mineralogy, Texture
Mortar
9.7
20.7
Made in laboratory
Sand and cement
Fragmental limestone
30.3
54.5
Chicago Lyons, IL
mixture fragmental,
Dolomitic limestone
48.3
151.7
Northern Minnesota
porous Dolomitic
Taconite
41.4
234.4
Massachusetts
siliceous, finely
Amphibolites
33.6
124.1
Material
grained crystalline. 38
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 pointloaded 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.
Normalised Load (MPa)
16
Amphibolite
14 Crystalline limestone 12 Fragmental limestone
10 8
Taconite
6 4 2
T
0 0
0.005
0.01
0.015
0.02
0.025
Normalised Displacement (D/d)
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. 39
Table 3.4 Summary or point-load strengths and deformability [7] Type of material
Diameter (mm)
(in.)
K
(kN)
(MPa)
(mm)
( /d)
(m/kN)
Q
(X l0-5) Dolomitic
28.6
(1)
7.6
7.4
0.37
0.0131
32.5
0.74
limestone
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
55.9
(2)
10.7
2.7
0.79
0.0141
61.6
0.71
limestone
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
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
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
Taconite
Amphibolite
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. 40
Table 3.5 Effect of size on average point-load strength and deformability [7] Diameter Type of material
29mm (kN) (MPa)
Mortar
7.6
Amphibolit e Crystalline limestone Fragmental limestone Taconite Diameter Type of material
107mm (kN) (MPa)
(D/d)
Mortar Amphibolit e Crystalline limestone Fragmental limestone Taconite
15.3 64.3
1.32 6.36
58.4
(D/d)
K (m/kN) (×10
a
7.4
0.0124
18.5
9.4
9.1
0.0138
20.7
10.4
10.1
0.0146
20.2
10.7
8.3
0.0165
21.4
18.7
18.1
0.0197
22.8
0.8 4 0.8 3 0.7 6 0.7 4 0.7 7
51.56mm (kN) (MPa )
(D/d)
8.6
2.6
24.9
a
0.0181
K (m/kN ) (× 10 22.8
6.8
0.0122
24.9
0.75
39.4
7.3
0.0107
34.4
0.72
18.4
5.4
0.0130
26.0
0.92
33.4
11.3
0.0143
28.2
0.95
(D/d)
a
152mm (kN) (MPa)
a
0.011 0.019
K (m/kN) (×10 12.3 29.1
4.52
0.017
45.2
0.70
23.7
2.53
0.015
32.3
0.78
48.5
3.65
0.012
33.4
0.88
0.76 0.71
23.3 117. 7 104. 4 76. 6
0.71 4.21
0.014 0.074
K (m/kN) (×10 9.7 11.4
2.34
0.096
54.2
0.70
1.47
0.013
35.6
0.75
108. 3
2.12
0.010
38.7
0.76
Normalised Load (Mpa)
12 10 8 29 54 107 152
6 4 2 0 0
0.005
0.01
0.015
0.02
Normalised Displacement (D/d)
0.025
Fig.3.27. Effect of specimen size on ultimate strength and deformability. 41
0.94
0.72 0.77
3.8 Design Swing Jaw Plates The factors of importance in designing the size of jaw crusher’s plate are:
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 304 mm (12 in.) and bottom opening 51mm (2 in) = 1200 mm = 900 mm = 50 mm Table Table3.6. Dimensional Chart for Jaw Crusher [6] Model
A
B
C
D
E
F
Weight(Ton)
300X400 400
300
1050
1180
1300
700
2.8
300Χ600 600
300
1750
1680
1680
950
6.5
300X750 750
300
2050
1930
1850
1150
12
300Χ900 900
300
1850
2490
2350
1500
17.5
Fig.3.28 Overall Dimensions of Typical Jaw Crusher [32 32] 42
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. 43
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
u ( x, y, z ) = α1 + α 2 x + α 3 y + α 4 z v( x, y, z ) = α5 + α 6 x + α 7 y + α8 z …… (3.35) w( x, y, z ) = α9 + α10 x + α11 y + α12 z Here α 1 , α 2 ...α 12 are constants. By using the nodal conditions 44
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, u ( x , y , z ) = N i ( x , y , z ) Q3 i − 2 + N j ( x , y , z ) Q3 j − 2 + N k ( x , y , z ) Q3 k − 2 + N l ( x , y , z ) Q3 l − 2
Where Ni, Nj, Nk, Nl are given by Eq. (3.35).
( x, y , z ) N ( x, y , z ) N ( x, y , z ) N ( x, y , z ) j k l i
[ N ( x, y , z ) ] = N Where
(
)
1 N ( x, y, z ) = a +b x+c y +d z i i i i i 6V 1 N ( x, y , z ) = a j + b j x + c j y + d j z j 6V 1 N ( x, y , z ) = a +b x+c y +d z k k k 6V k k 1 N ( x, y , z ) = a +b x+c y+d z l l l 6V l l
( (
)
)
45
……(3.35) (3.36) ……
V is the volume of the tetrahedron can be obtained by following 1
x i 1 x j V= 1 x k 1 x l
y i y j y k y l
z i z j z k z l
…… (3.37)
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.
x
y
j
a = x i k x l x
j
y k y l j
z z
k z l
1 z
1 y
j
b = −1 y i k 1 y l x
j
c =− x 1 z i k k x 1 z l l
j
j
d =− x i k x l
y
j
y k y l
z j z k z l 1 1 1
……
(3.38)
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
u( x, y, z ) {U } = v( x, y, z) = [ N ]3 X 12 {Q}12 X 1 w( x, y, z )
……
(3.39)
Where
N i N = 0 0
0
0
Nj
0
0
Nk
0
0
Nl
0
Ni
0
0
Nj
0
0
Nk
0
0
Nl
0
Ni
0
0
Nj
0
0
Nk
0
0
46
0 0 Nl
And
Q 3 i−2 Q3 i−1 Q3 i Q} = . . . Q3 l
{
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
∂u ε ∂x xx ∂ v ε ∂ y yy ε ∂w …… (3.40) ∂z zz {ε } = ε = ∂u ∂v = [ B ]6 X 12 {Q}12 X 1 xy ∂y + ∂x ε yz ∂v + ∂w ∂y ∂z ε zx ∂w + ∂u ∂z ∂x b i 0 0 1 [ B] = 6V c i 0 di
0
0
c i 0
0
j 0
d
0
j 0
c
b
b i d i 0
i 0
c i b i
b
j 0
d
j
0
0
c
0
d
j
j 0
b k 0
d
0
c
c k 0
j 0
b
j j
d
k
0
0
c k 0
0
b k d k 0
d
k 0
c k b k
b l 0 0 c l 0 d
l
0 c l 0 b l d l 0
The stress-strain relations, in the case of three-dimensional analysis, are given by 47
0 0 d l 0 c l b l
σ T = [ D ]{ε }
……
(3.41)
Where xx
σ T = σ
σ
yy
σ
zz
σ
xy
σ
yz
σ
zx
}
σT is the stress tensor and ξ is the strain displacement matrix
And [D] matrix can be defined as follows
ν ν 1 −ν ν ν 1 −ν ν ν 1 −ν E 0 0 0 [ D] = (1 + ν )(1 − 2ν ) 0 0 0 0 0 0
0
0
0 0
0 0
1 − 2ν 2
0
0
1 − 2ν 2
0
0
0 0 0 0 …… 0 1 − 2ν 2
(3.42)
The stiffness matrix of the element (in the global system) can be obtained as K ( e) = B T D B dV ∫∫∫ [ ] [ ][ ] Ve
…… (3.43)
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
K (e) = V (e) B T D B dV [ ] [ ][ ]
……
(3.44)
In this case, since the assumed displacement model is linear, the continuity of displacement along the interface between neighboring elements will be satisfied automatically.
48
CHAPTER -4
COMPUTATIONAL STUDY FOR SWINGING JAW PLATE AND SWINGING LEVER
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 applicationspecific 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 vectorbased 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: 49
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. 50
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. II. III.
Thickness = 140mm. Length = 1200mm. 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 51
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
Fig.4.5 swinging lever of the
Fig.4.6 assembled structure of
with three stiffeners
single toggle jaw crusher
swinging jaw plate with pitman
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.
52
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. 53
4.3.2 Computation In computation step the standard FE solutions procedures uses data provided by preprocessing 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 Fig.4.7 Finite Element In order to get a more accurate solution, the mesh
Analysis Process
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. 54
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
Swinging
Martensitic steel
jaw plate
(C-1.1%, Mn-13%)
Youngs
Yield
Poisions
Density
ratio
(Kg/m3)
modulus(GPa) strength(MPa) 210
550
0.266
7860
200
300
0.266
7860
Austenite steel Pitman
(C-0.04%, Mn-0.7%, Cr13%, Ni-4%,Mo-0.8% )
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
55
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 bolttightened 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. 56
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 57
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
0.311
0.262
0.212
0.18
0.164
0.16
Displacement (mm)
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 58
the toggle plate width can be taken as 800mm and the Von Misses stress and displacement are 98.6N/mm2 and 0.164mm respectively. 0.35
500 450
0.3
400
0.25
350
0.2 0.15
150
0.1
100
0.05
N/mm2
300
N/m 250 m2 200
50 0
0 100
200
mm 400 mm
600
800
900
100 200 400 600 800 900
mm
Fig.4.12 Vonmisses 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 strcture when the width of the toggle plate is considered at 100, 200, 400, 600, 800, 900mm.
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
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
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 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. 120 100
mm
N/mm2
80 60 40 20 0 0
100
mm
200
300
0.18 0.16 0.14 0.12 0.1 0.08 0.06 0.04 0.02 0 0
400
100
200
300
400
mm
Fig.4.20 Von Misses stress vs toggle location
Fig.4.21 displacement vs toggle location
62
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
63
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
64
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
65
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. Von Misses stress
Displacement(deformation)
(N/mm2)
(mm)
1
158
0.836
2
68.3
0.145
3
53.9
0.0883
Number of stiffeners
Table.4.3 Von Misses stress and displacement, swinging jaw plate with stiffeners.
66
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
67
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
Deformation by
Deformation by
% of Error
(mm)
Chrlesh H. Dowding
Present model
(mm)
(mm)
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.
68
CHAPTER -5
RESULTS, DISCUSSION AND CONCLUSION
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= M au 2 + av 2 = M au 2 + av 2
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. 2.0E+04
1 2
mm/s2
1.6E+04
3 4
1.2E+04
5 6
8.0E+03
7
4.0E+03
8 9
0.0E+00
10
0
120
240 Ф(Degrees)
360 11
Fig.5.1 Force distribution on the swinging jaw plate considering X and Y direction accelerations
69
1
2.0E+04
2 1.6E+04
3
mm/s2
4 1.2E+04 5 6
8.0E+03
7 4.0E+03
8 9
0.0E+00 0
120
240
360
10 11
Ф(Degrees)
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.
70
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
71
Fig.5.4 Mass of two stiffeners jaw plate
Fig.5.5 Mass of three stiffeners jaw plate
72
No of stiffeners
Von Misses stress
Deformation
Mass of the jaw plate
(N/mm )
(mm)
(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
2
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%
73
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.
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6. REFERENCES 1. Anon “Design of Jaw Crusher Avoids Toggles”, Minerals Engineering, Volume3, Issue 6, March 1999 Pages571-580. 2. Taggart, Arthur F “Hand Book of Ore Dressing”, John Willey & Sons Inc, 1998, Pages 255-280. 3. Lindqvist M., Evertsson C. M. “Liner wear in jaw crushers”, Minerals Engineering, Volume 16, Issue 1, January 2003, Pages 1-12. 4. DeDiemar R.B. “New concepts in Jaw Crusher technology”, Minerals Engineering, Volume 3, Issues 1-2, 1990, Pages 67-74. 5. Russell A.R., Wood D. M. “Point load tests and strength measurements for brittle Spheres”, International Journal of Rock Mechanics and Mining Sciences, Volume 46, Issue 2, February 2009, Pages 272-280. 6. Gupta Ashok, Yan D.S. “Mineral Processing Design and Operation-An introduction”, Published by Elsevier, 2006, Pages 99-127. 7. Dowding Charles H, Molling R, Ruhl C," Application of point load-deformation relationships and design of jaw crusher plates”, International Journal of Rock Mechanics and Mining Sciences & Geomechanics, Volume 20, Issue 2, April 1983,Pages 277-286. 8. Berry P, Dantini E.M. and Masacci, P. “Influences of Mechanical Characteristics of Rock on Size Reduction Processing”, Proceedings of Mineral Processing and Extractive Metallurgy, Beijing, January 1984, Pages 15-26. 9. Weiss N.L., “Jaw Crusher”, SME Mineral Processing Handbook, New York, 1985, Chapter 3B-1, Pages 245-261. 10. Niles I. L., “MS Thesis -Point Load Strength: Jaw Crusher Design”, August, 1978. 11. Georget Jean-Pirrre, Lambrecht Roger “Jaw Crusher” United States Patent, Patent Number 4, 361, 289, Issued on November, 1988. 12. Pollitz H C, “Crusher Jaw Plates” United States Patent, Patent Number 3,140,057, Issued on July, 1982. 13. Zhiyu Qin, Ximin Xu, “A Method of Optimization of the Mechanism of Compound Swing Jaw Crusher”, Journal of Taiyuan Heavy Machinery Institute, July1992. Pages 255-263.
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14. Cao Jinxi, Qin Zhiyu, Wang Guopeng, “Investigation on Kinetic Features of MultiLiners in Coupler Plane of Single Toggle Jaw Crusher”, Journal of Taiyuan Heavy Machinery Institute, July200.Pages 210-219. 15. Lytwynyshyn G. R., “MS Thesis-Jaw Crusher Design”, Northwestern University, Evanston, August1990. 16. Cao Jinxi, Rong Xingfu, Yang Shichun, “Jaw Plate Kinematical Analysis For Single Toggle Jaw crusher Design”, Journal of Taiyuan Heavy Machinery Institute, 2006.Pages 62-66 17. Gabor M. Voros “Finite element analysis of stiffened plates” Mechanical Engineering Volume51Issue2, 2007, Pages 105-112. 18. Kadid Abdelkrim “Stiffened Plates Subjected to Uniform Blast Loading” Journal of Civil Engineering and Management, Volume14, Issue3, July 2008, Pages155–161. 19. Bharule Ajay Suresh, “M.Tech Thesis Computer Aided Design and Analysis of Swing Jaw Plate of Jaw Crusher”, NIT Rourkela, June 2009. 20. Hansen L. Scott “Applied CATIA V5R15” Industrial Press, New York, USA, 2006, Pages 1-475. 21. Joseph R.P.“Austenitic Manganese Steel” ASM Handbook of Properties and Selection; Iron, Steel and High Performance alloys, Volume 1, Edition10, 1990, Pages 822-840. 22. Mukhopdhyay M, Sheikh A. B, “Matrix and Finite Element Analyses of Structures” Ane Books, New Delhi, 2004, Pages 408-413. 23. Rao S. S., “The Finite Element Method in Engineering”, Butterworth-Heinemann, Edition 4, Dec 2004. 24. Timoshenko S. and Goodier J. N, “Theory of Elasticity”, Tata McGraw-Hill, New York, 2001. 25. Tickoo Sham “Catia for Engineers and Designers V5R15”, DreamTech Press, Germany, 2000. 26. http://www.mistryjawcrusher.com/full-images/681579.jpg 27. http://www.vibratingfeederchina.com/blog/category/knowledge 28. http://nucat.library.northwestern.edu/cgi-bin/Pwebrecon.cgi784772 29. http://www.kolbergpioneer.com/jaw crusher data/specifications 30. http://www.westpromachinery.com/jaw crusher/components/jaw plates 31. http://www.sbmchina.com/jaw crusher/working principle/structure characteristics 32. http://www.harisonjawcrusher.com/crusher-model.htm 76
