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UNIVERSITY OF NAIROBI
COLLEGE OF ARCHITECTURE AND ENGINEERING
DEPARTMENT OF MECHANICAL AND MANUFACTURING
ENGINEERING
SMALL SCALE MECHANISED STONE CRUSHER: MECHANICAL
ANALYSIS
A final year project report submitted in partial fulfillment for the award
Of
The Bachelor of Science in Mechanical and Manufacturing Engineering
AUTHORS: MWAURA PAUL KAMAU F18/1431/2010
NJUGUNA JOSEPH MAINA F18/38300/2011
WANGARI JOSEPH NJANE F18/1415/2010
SUPERVISORS: PROF. MOSES .F. ODUORI
ENG. DAVID .M. MUNYASI
PROJECT CODE: MFO 02/2015
i
DECLARATION
We certify that the information presented in this report, except where indicated and acknowledged, is our
original effort and has not been presented before to the best of our knowledge.
MWAURA PAUL KAMAU DATE
NJUGUNA JOSEPH MAINA DATE
WANGARI JOSEPH NJANE DATE
This project has been submitted with our approval as university supervisors:
PROF. ODUORI. M. FRANK DATE
ENG. MUNYASI .M. DAVID DATE
ii
ACKNOWLEDGEMENT
We are grateful to the Almighty God for giving us the strength to carry out our final year project.
We also thank our loving families and friends who have given us constant encouragement,
support and guidance throughout the project period.
We thank the University of Nairobi through the department of Mechanical and Manufacturing
Engineering for facilitating our project.
We also owe our profound gratitude to our project supervisors Prof. M.F. Oduori and Eng.
Munyasi who took keen interest on our project work and guided us all along, till the completion
of our project by providing us with all the necessary information that we required.
iii
ABSTRACT
Kenya’s Vision 2030 development program launched in June 2008 to help transform the country
into a newly industrialized, middle-income country by 2030 focuses on the development in
sectors such as infrastructure, energy and other sectors. There is a need to crash rocks or ores and
reduce them to appropriate sizes in both the infrastructure and energy sectors that will drive the
country towards the realization of Vision 2030. It is with this perspective in mind that this report
seeks to determine the jaw crusher mechanism that is most efficient and hence use it for the
design of a small-scale mechanized jaw crusher.
This is achieved by performing a kinematical analysis on the double-toggle mechanism after
which a static force transmission analysis is done for the same mechanism from which the static
force transmission characteristics of the double-toggle mechanism are obtained. Based on similar
analyses previously done for the single-toggle jaw crusher and the horizontal pitman jaw crusher,
a suitable mechanism for the design of the small-scale mechanized jaw crusher is selected from
the three mechanisms.
Keywords: jaw crusher, double-toggle, single-toggle, horizontal pitman, kinematical analysis,
static-force analysis.
iv
TABLE OF CONTENTS
DECLARATION……………………………………………………………………………І
ACKNOWLEDGEMENT………………………………………………………………… II
ABSTRACT………………………………………………………………………………...III
CHAPTER 1………………………………………………………………………………….1
1.0) Introduction………………………………………………………………………………1
1.1) Statement of the Problem…………………………………………………………………3
1.2) Objectives……………………………………………………………………………...…4
1.3) Project Justification………………………………………………………………………5
1.4) Field Study…………………………………………………………………………….…6
1.4.1) Case Study Report (Madini House)…………………………………………….....6
1.5) Methodology…………………………………………………………………………...…9
CHAPTER 2……………………………………………………………………………...…10
2.0) Literature Review……………………………………………………………………….10
2.1) Stone Crushers…………………………………………………………………………..10
2.2) Jaw Crushers…………………………………………………………………………….12
2.3) Blake Type Jaw Crusher………………………………………………………………...12
2.3.1) Single-Toggle Jaw Crusher……………………………………………………..12
2.3.2) Double-Toggle Jaw Crusher…………………………………………………….14
2.4) Difference Between Single and Double-Toggle Jaw Crushers…………………………16
CHAPTER 3………………………………………………………………………………...17
3.0) Kinematical Analysis of the Double-Toggle Jaw Crusher Mechanism…………………17
3.1) Introduction……………………………………………………………………………..17
3.2) Kinematical Model……………………………………………………………………...18
3.3) Kinematical Analysis……………………………………………………………………20
3.3.1) Vector Loop Closure for the First Loop………………………………………..20
3.3.2) Vector Loop Closure for the Second Loop…………………………………….22
3.3.3) Angular Displacement of the Swing Jaw……………………………………....24
v
3.3.4) Angular Displacement of the Pitman…………………………………………..29
3.3.5) Angular Displacement of the Front Toggle Link……………………………....31
CHAPTER 4……………………………………………………………………………..….34
4.0) Static Force Analysis of the Double-Toggle Jaw Crusher Mechanism………………...34
4.1) Crank Analysis…………………………………………………………………………..35
4.2) Toggle Mechanism Analysis…………………………………………………………....36
4.3) Swing Jaw Analysis……………………………………………………………………..38
4.4) Application and Discussion of the Results of the Static Force Analysis……………….39
CHAPTER 5………………………………………………………………………………...41
5.0) Discussion………………………………………………………………………………41
5.1) Basis for Selecting a Suitable Crusher Mechanism…………………………………….41
5.2) Torque Transmission Characteristics for Different Jaw Crushers……………………...44
5.3) Conclusion……………………………………………………………………………....47
5.4) Recommendations………………………………………………………………………48
5.5) Further Scope of Study…………………………………………………………………49
REFERENCES……………………………………………………………………………..50
APPENDIX
vi
LIST OF TABLES
Table 1: Different crusher types and their applications.
Table 2: Data for a DB 6-4 (425×600) double-toggle jaw crusher.
Table 3: Analytically determined values of θ4 for given values of θ2.
Table 4: Analytically determined values of θ6 for given values of θ2.
Table 5: Analytically determined values of θ3 for given values of θ2.
Table 6: Analytically determined values of θ5 for given values of θ2.
Table 7: Reduction ratios of different types of crushers.
vii
LIST OF FIGURES
Figure 1: Gyratory crusher.
Figure 2: Jaw crusher.
Figure 3: Cone crusher.
Figure 4: Impact crusher.
Figure 5: Dodge type jaw crusher.
Figure 6: Blake type jaw crusher.
Figure 7: Double-toggle jaw crusher.
Figure 8: Typical cross-section of a swastick jaw crusher.
Figure 9: The Blake double-toggle jaw crusher design concept.
Figure 10: Kinematical model for the double-toggle mechanism.
Figure 11: First vector loop.
Figure 12: Second vector loop.
Figure 13: Variation of toggle angle, θ4 with crank angle θ2.
Figure 14: Variation of swing jaw angle θ6 with crank angle θ2.
Figure 15: Variation of Pitman angle θ3 with crank angle θ2.
Figure 16: Variation of Front toggle angle θ5 with crank angle θ2.
Figure 17: Model for static force analysis.
Figure 18: Force body diagrams of the moving links.
Figure 19: Balance of moments on the crank.
Figure 20: Triangle of forces in the toggle mechanism.
Figure 21: Balance of moments on the swing jaw.
Figure 22: Variation of normalized torque ratio with crank angle, θ2 for the double-toggle.
Figure 23: Variation of normalized torque ratio with crank angle, θ2 for the horizontal pitman.
viii
Figure 24: Torque ratio T3/T2 for the single-toggle jaw crusher.
ABBREVIATIONS AND SYMBOLS
θi - Angle of each member relative to the vertical in the counter-clockwise direction.
ri - Length of each coupler link.
Z- Horizontal axis direction.
Y- Vertical axis direction.
Oi – Revolute joints
α - Angular acceleration.
Fi- Force experienced by each member.
Fy- Force resolved in the vertical direction.
Fz - Force resolved in the horizontal direction.
T - Torque on the members.
Where i= 1, 2, 3, 4...
1
CHAPTER ONE
1.0) INTRODUCTION.
Crushing is a process of reducing the size of solid particles into definite smaller sizes by use of
mechanisms such as jaw crushers. The jaw crushers are major size reducing machines used in
mechanical, metallurgical and allied industries such as quarries, mining, ore crushing and
recycling industries. The crusher reduces the size of the feed by use of moving units against a
stationary unit or against another moving unit by applying pressure, impact, shearing or combine
action. The sizes range from 0.1 ton/hr to 50 ton/hr (Ministry of Mining Madini house). Notably
there are primary, secondary and fine crushers depending on the size reduction factor, in the
primary crusher, raw material from the mines is processed, here the input is relatively wider and
the output products are smaller in size, examples include jaw crusher and gyratory crusher. For
the secondary crusher, the output from the primary crusher is further reduced for fine crushing
examples include: cone crusher, gyratory crusher, spring rolls and disk crusher. Fine crushers
have relatively small openings and are used to crush the feed material into more uniform and fine
products an example is the gravity stamp.
The crushing activity has become an important sector engaged in producing crushed aggregates
of various sizes depending upon the requirement which acts as raw material for various
construction activities such as roads, highways, bridges and the buildings sector. A lot of
emphasis has been in the construction and the mining industry, evident by the heavy investment
by private sector and the Government, to this end direct employment opportunities have been
created and raised the profile of Kenya towards middle level income earners. Most of the
flagship projects depend on the construction and mining sector for supply of raw materials such
as aggregates to be completed and hence stone crusher equipments are needed. It is estimated
that there are 4,660 numbers of stone crushers in Kenya (Madini House). The number is
expected to grow further keeping in view the future plans for development of infrastructure,
mining and construction, that are required for overall development of the country. The stone
crushing industry is estimated to be providing direct employment to over 500,000 (Madini
house.) people engaged in various activities such as, crushing plant, transportation of mined
stones, construction and selling of crushed products etc. Most of these personnel are from rural
and economically challenged areas where employment opportunities are limited and hence it
2
carries greater significance in terms of social and economic importance to both rural and urban
development.
The quarrying sector has continually used technology which has been overtaken by time, the
tools used are a challenge to the personnel and they usually involve the breaking down of rocks
by simple hand tools (hammer and anvil) in small scale. These techniques are largely labor
intensive, produce inconsistencies in the aggregates that are produced and are limited in terms of
the production capacities since they depend on human performance, it is evident that, the sector
has great potential and hence needs utmost attention to improve mechanisms in use. There are a
number of factors that will play a role in the determination of what technologies will be applied,
notably, the physical and chemical characteristics of the rocks to be crushed are one of these
factors. Another factor is the geological characteristics of the rock in which the governing factors
are the hardness of the rocks, the structural components of the rock and the abrasive nature of the
rock amongst other factors. The consideration also lies in the output that one seeks. Different
technologies provide different end products which may be suitable for different forms of
applications. One factor that will be of consideration in this paper is as regards the type of
technology that will be applied.
Stone crushers are mainly categorized depending on the pivoting mechanism of the swing jaw. In
this major category we have the Blake crusher which is pivoted at the top which provides it with
fixed amount of feed. This is then further categorized into the double-toggle and the single-
toggle stone crushers. The construction of the double-toggle jaw crusher enables its application
as a crusher for strong abrasive rocks. The other two varieties are the dodge crusher which is
pivoted at the bottom to provide fixed delivery and is limited to laboratory use. There is also the
universal crusher that is pivoted at the mid position of the swinging jaw (Mular et.al. 2002).
Finally the stone crusher is able to provide consistency in the output which can be controlled
with certain types of crushers as desired. This is especially important in the construction industry
where the aggregate size determines the strength properties of the concrete used. Despite these
advantages there is the need to study the application of the stone crusher to determine its
effectiveness in the application to which it has been placed under.
3
1.1) Statement of the Problem
It is the aim of this project to choose a suitable mechanism that can be applied in the design of a
small-scale mechanized stone crusher. To achieve this, the kinematical and static force
transmission analysis of the double-toggle jaw crusher mechanism is performed. Thereafter, the
characteristics so obtained from the analysis of the double toggle mechanism are then compared
with those of the horizontal-pitman and single-toggle jaw crushers in order to assist in the
selection of the most suitable mechanism to be utilized.
Moreover, the selection criteria for a suitable mechanism should also consider the following
factors;
1.) Will it produce desired output size and shape at the required capacity?
2.) Will it accept the largest input size expected?
3.) What is its capacity?
4.) Will it choke or plug?
5.) Can it pass uncrushable debris without damage to the crusher?
6.) How much supervision of the unit is necessary?
7.) Will it meet product specifications without additional crushing stages and auxiliary
equipment?
8.) What is the crusher’s power demand per ton per hour of finished product?
9.) How does it resist abrasive wear?
10.) Does it operate economically with minimum maintenance?
11.) Does it offer dependable and prolonged service life?
12.) Is there ready availability of replacement parts?
13.) Does it have acceptable parts replacement cost?
14.) Does it have easy access to internal parts?
15.) Is the crusher versatile?
16.) How does the initial cost of the machine compare with its long term operating costs?
17.) Is experienced factory service readily available?
4
Therefore, it is with the above considerations in mind that the project seeks to select a crushing
mechanism that is best suited for use in small-scale mechanized jaw crusher.
1.2) OBJECTIVES
The objectives of the proposed project are grouped into two categories
Overall
i. To perform a kinematic analysis for a double-toggle jaw crusher mechanism that
describes the motion of the swing jaw.
ii. To perform a static force transmission analysis for a double-toggle jaw crusher
mechanism.
iii. To select a suitable mechanism for the design of a small-scale mechanized jaw crusher.
Specific objectives
i. To obtain equations that will describe the motion of any given point in the swing jaw
of a double toggle jaw crusher by reducing it to a planar mechanism.
ii. To obtain equations that will relate the torque applied to the torque available for
crushing in a double-toggle mechanism.
iii. To draw a comparison between the single-toggle, double-toggle and horizontal
pitman jaw crushers clearly illustrating the preferred mechanism for further
development of a small scale mechanized jaw crusher.
iv. To document results of the project for subsequent use in the development of a small-
scale mechanized jaw crusher.
5
1.3) PROJECT JUSTIFICATION
The design and development of a small scale stone crusher serves to solve the disparity between
the large scale and manual stone crushing since it will reduce the human effort requirements and
increase output. There is widespread demand for crushed stones as a result of the increasing
technological advancement and need for better infrastructure. The implementation of the design,
will contribute towards alleviation of the rural-urban migration since the stone crushing activity
is an income generating activity.
The motion of the swing jaw in a double-toggle crusher is such that it applies an almost purely
compressive force upon the material being crushed. This minimizes wear on the crushing
surfaces of the jaws and makes the double toggle jaw crusher suitable for crushing highly
abrasive and very hard materials. It’s paramount to study the mechanism involved during
operation and be able to perform both a kinematical and static force analysis for the mechanism,
the study will be useful in determining the loading and throughput in the crushing zone. The
investigators have sought previous study, but the resource materials were limited, other work and
presentations that have studied the double toggle jaw crusher have not provided the useful
information. Cao et. al. (2006) gave a presentation of the kinematic analysis of the single-toggle
jaw crusher dealing with the mechanism of fracture of the material being crushed, the wear of the
crushing jaw surfaces and a list of the kinematical equations involved, which did not apply to the
double-toggle mechanism.
The first double-toggle jaw crusher was designed by Eli Whitney Blake in the USA 1857 (Mular
et .al.2002). Ham Crane and Rodgers (1958) performed a static force analysis for a double-toggle
jaw crusher but did not perform a kinematical analysis for it, likewise, Martin (1982) also
featured the double toggle jaw crusher as an example of a toggle mechanism but did not perform
a kinematic analysis for the mechanism
In this aspect, analysis of the double-toggle mechanism has caught the interest of the
investigators; here the vector loop closure method will be used to develop a kinematic analysis
for the double-toggle jaw crusher mechanism. This method will enable the derivation of the
6
necessary equations of motion from first principles. This work will provide useful information on
both the kinematic and static force analysis of the crusher which has not been easy to find.
1.4) Field Study
The field study was carried out in form of question- answer sessions with the respondents as well
the investigators participation for clarity. Questions forwarded to acquire useful information
were
a. What are the techniques and mechanisms used in stone crushing?
b. What is the throughput per day?
c. What are the advantages and challenges of the method used in crushing?
d. What is the cost of a stone crushing machine?
e. What is the market demand for aggregate in the specific location?
f. Is there any other technique that could be employed should the need arise?
g. What are the stakeholder involvements in funding research for similar projects?
The areas visited were the Ministry of mining at Madini House (Industrial area), Approtech
super money market (Kariobangi), Jua Kali Association shed (Gikomba Market) and Thika
Makogeni quarry in Kiambu County. Our case study base was Madini house.
1.4.1) Case study report (Madini house)
Visits to Madini house under the Ministry of Mining were so as to source more information on
the toggle designs used in the field. The machines used were primary, secondary jaw crushers
and laboratory roller crushers. These machines reduce the size of rocks to 25, 12.5 and 3.25 mm
respectively. The information about the crushers was limited since the core business of the
premise is to analyze the minerals after crushing. These machines were installed in 1975,
machine manuals were not available.
However the investigators were able to read off the power ratings, speed and capacity of the
machines for comparison purposes, also the nature of rocks crushed and the processes involved
before final mineral analysis was demonstrated by technical personnel, Mr. Wambua the Chief
Technologist.
7
Visit to Madini house and photos of primary crusher and rocks of different hardness
8
Roller crusher
Laboratory crusher secondary crusher
9
1.5) Methodology
Literature concerning various types of jaw crushers and their method of operation was
sourced and relevant information pertaining to the project was documented.
A kinematical analysis for the double-toggle jaw crusher mechanism was performed and
equations pertaining to the motion of the swing jaw were formulated and graphs to
analyze these motions were drawn.
A static force analysis for the double-toggle jaw crusher mechanism was performed in
which the static force transmission characteristics of the mechanism were determined.
Comparison of the single-toggle, double-toggle and horizontal pitman crusher
mechanisms was done in which a suitable mechanism for application in the design of a
small-scale mechanized jaw crusher was selected.
A discussion about the selected mechanism was done and a conclusion concerning the
mechanism was finally drawn.
10
CHAPTER TWO
2.0) LITERATURE REVIEW
2.1) STONE CRUSHRES
Different types of crushers exist depending on their design and crushing mechanism. These
include:
i. Jaw crushers,
ii. Gyratory crushers.
iii. Cone crushers.
iv. Impact crushers.
A crusher may be considered as primary or secondary depending on the size reduction factor.
Jaw and gyratory crushers, are primary crushers, here the input is relatively wider and output
products are coarser in size. On the other hand, secondary crushers have a feed size usually less
than 15cm and reduce the stones to the required sizes examples include Cone crushers and
impact crushers. Fine crushers such as gravity stamp have relatively small openings and are used
to crush the feed material into more fine uniform and fine products. The different crushers are
shown below
Fig 1. Gyratory crusher Fig 2. Jaw Crusher
11
Fig 3. Cone Crusher Fig 4. Impact Crusher
The choice between the jaw crusher and gyratory crusher is dictated by the largest feed size,
production requirements, and the economics of operation.
Table 1. Different crusher types and their applications.
Type hardness Abrasion
limit
Reduction
ration
Main use
Jaw crusher Soft to very
hard
No limit 3/1 to 5/1 Quarried materials,
sand gravel
Gyratory
crusher
Soft to hard Abrasive 4/1 to 7/1 Quarried materials
cone crusher Medium to
very hard
Abrasive 3/1 to 5/1 Sand gravel
Horizontal shaft
Impactors
Soft to
medium hard
Slightly
abrasive
10/1 to 25/1 Quarried materials,
sand gravel, recycling
Impactors(shoe
and anvil)
Medium to
very hard
Slightly
abrasive
6/1 to 8/1 Sand gravel, recycling
12
2.2) JAW CRUSHERS
They are classified according to the amplitude of motion of the moving face.
2.3) Blake Type Jaw Crusher
Blake type jaw crusher, primary crushers in the mineral industry; attains maximum amplitude at
the bottom of the crushing jaws as the swinging jaw is hinged at the top of the frame. These
crushers are operated by and controlled by a pitman and a toggle. The feed opening is called
gape and opening at the discharge end termed as the set. The Blake crushers may have single or
double toggle stone crusher. The toggle is used to guide the moving jaw. The retrieving motion
of the jaw from its furthest end of travel is by springs for small crushers or by a pitman for larger
crushers. During the reciprocating action, when the swinging jaw moves away from the fixed jaw
the broken rock particles slip down and are again caught at the next movement of the pitman and
are crushed again to even smaller size. This process continued till the particle sizes becomes
smaller than set; the smallest opening at the bottom. For a smooth movement of the moving
jaws, heavy flywheels are used.
. Blake type jaw crusher may be divided into two types.
2.3.1) Single toggle jaw crusher: - A single toggle bar is used in this type of crushers.
Comparatively lighter jaw crushers use single toggle as they are cheap.
Fig 5. Dodge Type Jaw Crusher
13
i. The movable jaw is pivoted at the bottom and connected to an eccentric shaft. The
universal crushers are pivoted in the middle so that the jaw can swing at the top and the
bottom as well.
Maximum amplitude of motion is obtained at the top of the crushing plates. Dodge type crushers
are not used for heavy duty and are commonly found in laboratories.
Fig 6. Blake Type Jaw Crusher.
The mechanism of jaw crusher is based on the concept of “crushing without rubbing”. Jaw
crushers consist of two jaws. One fixed and the other reciprocating. The opening between them
is largest at the top and decreases towards the bottom. The pitman moves on an eccentric shaft
and the swing lever swings on centre pin. The rock is thrown between two jaws and crushed by
mechanical pressure.
A belt pulley; which is driven by a motor drives the eccentric shaft to rotate. This makes the
attached jaw to approach and leave the other jaw repeatedly, to crush, rub and grind the feed.
Hence the material moves gradually towards the bottom and finally discharges from the
discharge end. The fixed jaw mounted in a “V” alignment is the stationary breaking surface.
The swinging jaw exerts impact force on the material by forcing it against the stationary plate.
The space at the bottom of the “V” aligned jaw plates is the crusher product size gap or size of
14
the crushed product from the jaw crusher. The material is crushed repeatedly until it is small
enough to pass through the gap at the bottom of the jaws.
The ores are fed to the machine from the top where the jaws, are maximum apart. As the jaws
come closer the ores are crushed into smaller sizes and slip down the cavity in the return stroke.
In following cycle, further reduction of size is experienced and the ore moves down further. The
process is continued till particle size is reduced to less than the bottom opening.
The toggle is used to guide the moving jaw. The retrieving motion 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
movement of the moving jaws, heavy flywheels are used.
2.3.2) Double toggle jaw crusher
Double-toggle jaw crushers are equipped with a system of toggle levers, which is moved up and
down by a pitman via an eccentric shaft. The alternating stretching and bending movements
cause an oscillating motion of the swing jaw. Since the material to be crushed falls down by
gravitation, the pressure which is necessary to crush the material is generated as the swinging
jaw moves forward in the narrowing crushing chamber thereby exerting pressure on the rock by
forcing it against the stationary plate, the process is intensified by ridges on the crushing jaw
liners. When the swing jaw retreats, the crushed material exits the crushing chamber through the
pre-selected gap at the bottom, while new material slips down from the top. The space at the
bottom of the “V” aligned jaw plates is the crusher product size gap or size of the crushed
products from the jaw crusher while the maximum opening at the top is the gape.
The toggle lever system ensures a very good power transmission from the drive unit to the
crushing tools making double-toggle jaw crushers the ideal machines for the crushing of the
hardest and toughest materials. Even with very abrasive materials minimum wear is observed.
Hence the ability to crush materials is excellent for tough and abrasive minerals, notable
characteristics are.
Large, rough, massive and sticky rocks can be crushed.
They are easy to maintain
It is very simple to adjust and prevent excessive wear and are easy to repair,
Moving jaw can be reinforced with high tensile manganese to crush very hard rock
15
Fig 7. Double Toggle Jaw Crusher Schematic Diagram
Fig 8
16
2.4) Difference Between Double-Toggle and Single-Toggle Jaw Crushers
Single-toggle jaw crushers are smaller in size and lighter. They have fewer shafts and bearings
and only one toggle plate connecting the bottom of the swing jaw to a fixed point at the back of
the jaw crusher. The eccentric shaft is located at the top of the swing jaw .The advantage of this
is that the jaw has two motions occurring at the same time. It has the same swinging door motion
that the double toggle has, but also has the up and down motion from the eccentricity of the shaft
which increases productivity.
In contrast, double-toggle jaw crushers are much larger, heavier and have more moving parts and
lower throughput than modern single-toggle jaw crushers. The lower throughput statement is a
bit misleading because it is partially attributed to the type of bearings they have versus modern
crushers, so if one was to upgrade the bearings, throughput could be closer to that of a modern
single-toggle jaw crusher.
Double-toggle jaw crushes are more about where the eccentric is located than anything else. In a
double-toggle jaw crusher, the eccentric is located behind the swing jaw. This has two main
effects; it keeps the eccentric safely out of danger because no shock loading from the rock being
crushed will be transferred to the eccentric shaft and bearings. The other effect is a limited plane
of motion for the swing jaw which contributes to its reduced productivity. The jaw moves like a
swinging door that is hinged at the top and is being pushed open and pulled closed at the bottom.
One toggle plate connects the bottom of the eccentric arm to the bottom of the swing jaw while
the other toggle plate connects the opposite side of the bottom of the eccentric arm to a fixed
point at the back of the jaw crusher frame.
17
CHAPTER THREE
3.0) Kinematic Analysis of the Double-Toggle Jaw Crusher Mechanism.
3.1) Introduction
The aim of any kinematic analysis of a mechanism is to determine the output motion, given the
input motion and the kinematical parameters of the mechanism. For the double-toggle
mechanism; the input motion is the rotation of the eccentric shaft, the kinematical parameters
refer to the effective lengths of the links that comprise the mechanism, and, the output motion is
the resulting motion of the swing jaw.
Kinematical analysis of a mechanism can be done through graphical, analytical and computer
aided methods. For this case, analytical methods which result in a small number of equations that
contain all the information that is required to completely describe the kinematics of the system
are used.
All points in the crushing mechanism of the double-toggle jaw crusher are constrained to move
in parallel lines. Moreover, the mechanism consists of six links, namely; the eccentric, the swing
jaw, two toggle links, the pitman and the frame, in the form of two closed kinematic chains. All
joints in the mechanism are revolute joints. Thus, each of the two kinematic chains of the
mechanism can be modeled as a planar four-bar mechanism with four revolute joints. Further,
the analysis of the mechanism recognizes the following two constraints:
All the links in the mechanism are assumed to be completely rigid. Therefore, the
effective lengths of the links remain invariant throughout the cycle of motion of the
mechanism.
The two kinematic chains that constitute the mechanism remain closed throughout the
cycle of motion of the mechanism.
As a result of the above constraints, for any phase of motion of the mechanism, the effective
lengths of the links can be taken to be vectors, of known magnitudes, that form two closed loops.
18
Consequently, a vector loop closure equation for each of the two loops can be written for the
mechanism. Beyond this, the analysis of the mechanism is reduced to mathematical routine.
3.2) Kinematical Model
The concept of the double toggle jaw crusher is illustrated in Fig. 9. The swing jaw drive
mechanism, which includes the eccentric shaft, the pitman, the toggle links, the swing jaw and
the frame, can be modelled as a planar six bar mechanism (Erdman and Sandor, 1991; Kimbrell,
1991; Shigley and Uicker, 1980).
Fig. 9 – The Blake Double Toggle Jaw Crusher Design Concept
Rotation
Oscillation Eccentric
Swing Jaw
Toggle Toggle
Pitman
Frame
Aggregates
Stationary Jaw
In the kinematical model, which is illustrated in Fig. 10, the eccentric shaft is modeled as a short
crank, of length 2r , that continuously rotates about a fixed axis, at 2O . The pitman is modeled
as the coupler link 43OO , of length 3r , which moves with a complex planar motion that has
both rotational and translational components. The toggle link of length 4r rocks about the fixed
axis at 1O . The toggle link of length 5r is modeled as the coupler link 54OO which also moves
with a complex planar motion that has both rotational and translational components. The swing
jaw is modeled as the rocker 65OO , of length 5r , which oscillates about the fixed axis at 6O .
19
The fixed jaw is considered to be an integral part of the frame of the machine. Thus, two closed
loops, 14321 OOOOO and 16541 OOOOO , can be identified in the kinematical model.
In studying the kinematics of the double toggle jaw crusher, it is particularly important to
understand the motion of the rocker link 65OO , relative to the fixed jaw, as the crank rotates
through a complete cycle. A right-handed Cartesian reference frame that is convenient for
analyzing this motion will be used, as shown in Fig. 10. The X axis is perpendicular to the
plane of the figure and it points at the reader. Angular displacements are taken counter-
clockwise, relative to the positive Y direction.
Fig. 10 – Kinematical Model
3O
1r
3r
2
5r
6r
6
Y
Z
1O
2O
5O
6O
4
4r
2r
4O
7r
20
3.3) Kinematical Analysis
3.3.1) Vector Loop Closure for the First Loop
The analysis of position and displacement can be accomplished through the use of the well
known vector loop closure method (Erdman and Sandor, 1991; Kimbrell, 1991; Shigley and
Uicker, 1980). The first loop to be treated is illustrated in Fig. 11. The vector loop closure
equation can be written as follows:
04321 rrrr (1)
Equation (1) can be re-written in complex notation as follows:
43214321
jjjjerererer = 0 (2)
Fig. 11 – First Vector Loop
3O
1r
3r
2 Y
Z 1O
2O
4
4r
2r
4O
31
Moreover, the Euler identities state as follows (Carmichael and Smith, 1962):
sincos
sincos
je
je
j
j
(3)
For conciseness, let us introduce the following notation:
21
ii
ii
s
c
sin
cos (4)
By using equations (3) and (4), equation (2) can be re-written as follows:
0444333222111 jscrjscrjscrjscr (5)
In equation (5), if the real terms and the imaginary terms are considered separately, the following
two equations are readily obtained:
44332211
44332211
srsrsrsr
crcrcrcr (6)
By squaring each of equations (6), the following is obtained:
2
4
2
44343
2
3
2
3
2
2
2
22121
2
1
2
1
2
4
2
44343
2
3
2
3
2
2
2
22121
2
1
2
1
22
22
srssrrsrsrssrrsr
crccrrcrcrccrrcr (7)
By adding corresponding terms in equations (7), and noting that 122 ii sc , the following is
obtained:
2
4434343
2
3
2
2212121
2
1 22 rssccrrrrssccrrr (8)
Now, equations (6) can be rearranged into the following:
44221133
44221133
srsrsrsr
crcrcrcr (9)
Moreover, it is known from trigonometry that (Carmichael and Smith, 1962):
kikiki cossinsincoscos (10)
By substituting equations (9) into equation (8), and using the identity in equation (10), the
following is obtained:
2442
2
4
2
3
2
2
2
114411221
cos2
cos2cos2
rr
rrrrrrrr (11)
In Fig. 11, 1 is a fixed quantity. Moreover, the motion of the crank 32OO is the input motion
and may be considered to be a rotation at uniform angular velocity, 2 . Thus, at an instant in
22
time, t , after commencement of the motion, the value of 2 , in radians, will be determined as
follows:
tt 22 )( (12)
For given values of 1r , 2r , 3r , 4r and 1 , equation (11) can be used to determine the value of
4 that corresponds to any given value of 2 . In that case, equation (11) will therefore describe
all the possible phases of motion of the mechanism whose vector loop is illustrated in Fig. 11.
In the special case where 01 , equation (11) reduces to the following:
2442
2
4
2
3
2
2
2
1441221 cos2cos2cos2 rrrrrrrrrr (13)
Each of the terms in equation (13) can be divided by 422 rr and the resulting equation can be re-
arranged to obtain the following:
24
42
2
4
2
3
2
2
2
12
2
14
4
1 cos2
coscos
rr
rrrr
r
r
r
r (14)
Equation (14) can be re-written as follows:
42
2
4
2
3
2
2
2
13
4
12
2
11
2434221
2
coscoscos
rr
rrrrK
r
rK
r
rK
KKK
(15)
Equation (15) is the well known Freudenstein’s equation that has been commonly used in the
synthesis of four bar mechanisms (Erdman and Sandor, 1991; Kimbrell, 1991; Shigley and
Uicker, 1980).
3.3.2) Vector Loop Closure for the Second Loop
The second loop to be treated is illustrated in Fig. 12. The vector loop closure equation can be
written as follows:
07654 rrrr (16)
23
Equation (16) can be re-written in complex notation as follows:
76547654
jjjjerererer = 0 (17)
By using equations (3) and (4), equation (17) can be re-written as follows:
0777666555444 jscrjscrjscrjscr (18)
In equation (18), if the real terms and the imaginary terms are considered separately, the
following two equations are readily obtained:
77665544
77665544
srsrsrsr
crcrcrcr (19)
By squaring each of equations (19), the following is obtained:
2
7
2
77676
2
6
2
6
2
5
2
55454
2
4
2
4
2
7
2
77676
2
6
2
6
2
5
2
55454
2
4
2
4
22
22
srssrrsrsrssrrsr
crccrrcrcrccrrcr (20)
Fig. 12 – The Second Vector Loop
5r
6r
6
Y
Z 1O5O
6O
4
4r4O
7r
5
7
24
By adding corresponding terms in equations (20), and noting that 122 ii sc , the following is
obtained:
2
7767676
2
6
2
5545454
2
4 22 rssccrrrrssccrrr (21)
Now, equations (19) can be rearranged into the following:
44776655
44776655
srsrsrsr
crcrcrcr (22)
By substituting equations (22) into equation (21), and using the identity in equation (10), the
following is obtained:
4664
2
7
2
6
2
5
2
474747676
cos2
cos2cos2
rr
rrrrrrrr (23)
In Fig.12, 7 is a fixed quantity. Moreover, given the motion of the crank 32OO , the
corresponding motion of the rocker 41OO , and hence 4 , can be determined by use of equation
(11). Once 4 is known, the corresponding value of 6 can be determined by use of equation
(23), so long as 4r , 5r , 6r , 7r and 7 are known. Thus, for given values of the lengths of all
the links in the mechanism, along with 1 and 7 , equations (11) and (23) contain all the
information that is necessary to determine all the phases of motion of the mechanism.
3.3.3) Angular Displacement of the Swing Jaw
For given values of the lengths of the four links, equation (11) can be used to determine the
values of 4 that correspond to given values of 2 .
The data in Table 2 shall be used to demonstrate application of the kinematical equations.
Table 2– DB 6-4 (425 by 600) Double-Toggle Jaw Crusher Dimensions
1r (mm) 2r (mm) 3r (mm) 54 , rr (mm) 6r (mm) 7r (mm) 1
(degrees)
7
(degrees)
662.5 28.5 609.5 503.5 1166 1537 45 40
By using the above data, equation (11) can be reduced to:
25
2223
222
221
23422421
sincos93.0211.11
sin437.16
cos437.16
sincos
f
f
f
fff
(24)
In equation (24), for given values of 2 , the functions 21 f , 22 f and 23 f take on
definite values, denoted by 1k , 2k and 3k , respectively and the following can be obtained from
equation (24):
2
2
2
3
31
2
2
2
1
442
2
0coscos
kkc
kkb
kka
cba
(25)
For any given value of 2 , the above equation can be solved to yield 2 values of 4 . Thus there
are two possible configurations of the four bar mechanism, whose vector loop is illustrated in
Figure 11, for any possible value of 2 .
However, only one of these configurations is applicable. By reviewing the configuration of the
double toggle jaw crusher mechanism, it should be evident that the applicable configuration of
the mechanism should not have a value of 3 that is substantially greater than zero, or a value of
4 that is somewhat close to zero.
Microsoft Excel was used to calculate the non-trivial values of 4 that correspond to given
values of 2 , for one complete cycle of rotation of the crank. A sample of the results is given in
Table 3 and the relationship between 2 and 4 is plotted in Fig. 13.
26
Table 3: Values of 4 for given values of 2
2 (Degrees) 4 (Degrees) 2 (Degrees) 4 (Degrees)
0 102.868 195 109.542
15 103.008 210 109.172
30 103.357 225 108.589
45 103.892 240 107.840
60 104.582 255 106.983
75 105.384 270 106.080
90 106.250 285 105.199
105 107.123 300 104.399
120 107.945 315 103.732
135 108.659 330 103.238
150 109.212 345 102.945
165 109.560 360 102.868
180 109.674
27
102
103
104
105
106
107
108
109
110
0 30 60 90 120 150 180 210 240 270 300 330 360
Angular Position of the Crank (Degrees)
Angula
r P
ositio
n o
f th
e R
ocker
(Degre
es)
Fig. 13 – Variation of Back Toggle Angle 4 with Crank Angle 2 .
Similarly, by using the data in Table 2, equation (23) may be reduced to the following:
169856.3sin84731.0cos01.1
sin9622.1
cos33845.2
sincos
4443
442
441
43642641
g
g
g
ggg
(26)
In equation (26), for given values of 4 , the functions 41 g , 42 g and 43 g take on
definite values, denoted by 1K , 2K and 3K , respectively and the following can be obtained
from equation (26):
2
2
2
3
31
2
2
2
1
662
2
0coscos
KKC
KKB
KKA
CBA
(27)
28
For any given value of 4 , the above equation can be solved to yield 2 values of 6 . Thus there
are two possible configurations of the four bar mechanism, whose vector loop is illustrated in
Figure 12, for any possible value of 2 . However only one of these configurations is applicable,
that is, the one giving values of 4 that are close to 090 and values of 6 that are close to
0180 , which should be evident by reviewing the configuration of the double toggle jaw crusher
mechanism.
Microsoft Excel was used to calculate the non-trivial values of 6 that correspond to given
values of 2 , for one complete cycle of rotation of the crank. A sample of the results is given in
Table 4 and the relationship between 2 and 6 is plotted in Fig. 14.
Table 4: Values of 6 for given values of 2
2 (Degrees) 6 (Degrees) 2 (Degrees) 6 (Degrees)
0 180.443 195 182.138
15 180.471 210 182.025
30 180.544 225 181.854
45 180.659 240 181.640
60 180.813 255 181.407
75 181.002 270 181.173
90 181.216 285 180.957
105 181.444 300 180.772
120 181.670 315 180.624
135 181.874 330 180.519
150 182.037 345 180.458
165 182.143 360 180.443
180 182.178
The minimum value of 6 is about 0443.180 at it occurs at a crank angle of zero. The
maximum value of 6 is about 0178.182 and it occurs at a crank angle of about
0180 . As can
29
be discerned in Table 4 and Figure 14 the range of variation of the inclination of the swing jaw to
the vertical is only about 0735.1 . With the length of the swing jaw being 1166 mm, this range
of angular oscillation of the swing jaw translates to a throw of about 35 mm at the lower end of
the swing jaw. However, the throw diminishes proportionately as we move from the bottom of
the swing jaw towards the pivot of the swing jaw, at which point it becomes zero.
180.4
180.6
180.8
181
181.2
181.4
181.6
181.8
182
182.2
0 30 60 90 120 150 180 210 240 270 300 330 360
Angular Position of the Crank (degrees)
Angula
r P
ositio
n o
f th
e S
win
g J
aw
(degre
es)
Fig. 14 – Variation of Swing Jaw Angle 6 with Crank Angle 2 .
3.3.4) Angular Displacement of the Pitman
Referring to the vector loop illustration in Fig. 11, it should be evident that, for given values of
2 , the angular position of the coupler link 43OO is determined as follows:
3
44221113
sinsinsinsin
r
rrr (28)
The data in Table 2 were used in a Microsoft Excel environment to calculate the values of 3
that correspond to given values of 2 , for one complete cycle of rotation of the crank. A sample
of the results is given in Table 5 and the relationship between 2 and 3 is plotted in Fig. 15.
30
In a completely symmetrical configuration of the pitman and the two toggle links, on would
expect the angular oscillation of the pitman to be symmetrically centred about the vertical (the
zero degrees line). However, from the results obtained here, it is evident that the angular
oscillation of the pitman is slightly skewed towards the negative angular direction and centred
around an angle of about 0415.1 . This result could be in part due to the fact that the lengths
of the links in the mechanism were determined through measurement that could be subject to
some small error. However, a deviation of less than 05.1 is acceptable for our purposes.
Table 5: Values of 3 for given values of 2
2 (Degrees) 3 (Degrees) 2 (Degrees) 3 (Degrees)
0 -2.106 195 -1.261
15 -1.386 210 -2.009
30 -0.674 225 -2.720
45 -0.015 240 -3.340
60 0.551 255 -3.821
75 0.990 270 -4.125
90 1.276 285 -4.230
105 1.392 300 -4.131
120 1.329 315 -3.838
135 1.088 330 -3.378
150 0.681 345 -2.786
165 0.131 360 -2.106
180 -0.531
31
-5
-4
-3
-2
-1
0
1
2
0 30 60 90 120 150 180 210 240 270 300 330 360
Angular Position of the Crank (degrees)
Angula
r P
ositio
n o
f th
e P
itm
an (
degre
es)
Fig. 15 – Variation of Pitman Angle 3 with Crank Angle 2 .
Angular Displacement of the Front Toggle Link
Referring to the vector loop illustration in Fig. 12, it should be evident that, for given values of
2 , the angular position of the front toggle link 54OO is determined as follows:
5
44667715
coscoscoscos
r
rrr (29)
The data in Table 2 were used in a Microsoft Excel environment to calculate the values of 5
that correspond to given values of 2 , for one complete cycle of rotation of the crank. A sample
of the results is given in Table 6 and the relationship between 2 and 5 is plotted in Fig. 16.
32
Table 6: Values of 5 for given values of 2
2 (Degrees) 5 (Degrees) 2 (Degrees) 5 (Degrees)
0 75.793 195 68.975
15 75.651 210 69.359
30 75.298 225 69.961
45 74.757 240 70.732
60 74.058 255 71.612
75 73.243 270 72.534
90 72.362 285 73.432
105 71.469 300 74.244
120 70.625 315 74.919
135 69.890 330 75.419
150 69.318 345 75.715
165 68.957 360 75.793
180 68.838
The values of 4 and 5 obtained in the above calculations indicate that the actual
configuration of the double toggle jaw crusher mechanism is more like the illustration in Fig. 9,
with 4 being an obtuse angle and 5 being an acute angle, rather than the illustration in Figs.
10, 11 and 12, in which 4 is acute and 5 is obtuse. However, Figs. 10, 11 and 12 are still
good enough for purposes of deriving the relevant kinematical equations.
33
68
69
70
71
72
73
74
75
76
0 30 60 90 120 150 180 210 240 270 300 330 360
Angular Position of the Crank (degrees)
Angula
r P
ositio
n o
f th
e F
ront
Toggle
(degre
es)
Fig. 16 – Variation of Front Toggle Angle 5 with Crank Angle 2 .
34
CHAPTER FOUR
4.0) Static Force Analysis of the Double Toggle Jaw Crusher Mechanism
The forces acting in the links of the double toggle jaw crusher mechanism are illustrated in Fig.
17 below.
Fig. 17 – Model for Static Force Analysis
1O4O
5O
6O
6T
2T
6F
6F
5F5F
4F
4F
3O
2O2F
2F
3F
3F
In performing the static force analysis it shall be assumed that the masses of the links, as well as
friction forces are negligible. In Fig. 17, 2T is the driving torque, applied about the crank axis
2O to drive the crank and the entire crusher mechanism. 6T is the torque, acting about the
swing jaw axis 6O , due to the resistance of the feed material against being crushed, and its value
shall be assumed to be predetermined. 2F , 3F , 4F , 5F and 6F are the forces in links 2, 3, 4, 5
and 6 respectively and they are all assumed to be compressive.
35
Static Force Analysis
The free-body diagrams of the moving links 2, 3 4, 5 and 6 are shown in Fig. 18, below.
However, it is convenient to show the toggle mechanism consisting of links 1, 3, 4 and 5 in a
partly assembled configuration as can be seen in Fig. 18.
Fig. 18 – Free Body Diagrams of the Moving Links
3O2T
2O
2F
2F
32ZF
32YFCrank(a)
4O
5O
5F5F
1O
4F
4F
3F
3F
3O 23ZF
23YF
65ZF
65YF
MechanismToggle(b)
6O
6T
6F
6F
56ZF
56YF
5O
JawSwing(c)
4.1) Crank Analysis
Let us start by considering the crank. The equilibrium of moments on the crank, about the joint
1O , leads to the following result:
36
22322322
222322232
sincos
cossin0
rFFT
TrFrF
YZ
ZY (1)
In equation (1), 2r is the length of the crank.
4.2) Toggle Mechanism Analysis
Next let us consider the assemblage that is labeled the toggle mechanism. The equilibrium of
forces at joint 3O requires that the following equations be satisfied:
332332
3323
3323
cos
cos
0cos
FFF
FF
FF
YY
Y
Y
(2)
332332
3323
3323
sin
sin
0sin
FFF
FF
FF
ZZ
Z
Z
(3)
From equations (1), (2) and (3), it follows that:
3223
2323
22332332
sin
sin
sincoscossin
rF
rF
rFFT
(4)
The statement of equation (4) is illustrated in Fig. 19, below.
Fig. 19 – Balance of Moments on the Crank
2O
2T 1O3F
2r
32
37
Similarly, equilibrium of forces at joint 5O leads to the following:
556556
5565
5565
cos
cos
0cos
FFF
FF
FF
YY
Y
Y
(5)
556556
5565
5565
sin
sin
0sin
FFF
FF
FF
ZZ
Z
Z
(6)
In Fig. 18, equilibrium of the forces acting at joint 4O requires that the vectors of the forces 3F ,
4F and 5F form a closed triangles since these three forces are concurrent at 4O . The closed
triangle is shown in Fig. 20.
Fig. 20 – Triangle of Forces in the Toggle Mechanism
3F
4F
5F
34
45
35180
Applying the sine rule to the triangle in Fig. 20 leads to the following result:
34
5
35
4
45
3
sinsinsin
FFF (7)
38
Hence:
45
3435
sin
sin
FF (8)
4.3) Swing Jaw Analysis
Now let us consider the swing jaw. The equilibrium of moments on the swing jaw, about the
joint 6O , leads to the following result:
66566566
666566656
sincos
90sin180sin0
rFFT
TrFrF
YZ
ZY (9)
From equations (5), (6) and (9), it follows that:
56656 sin rFT (10)
The statement of equation (10) is illustrated in Fig. 21, below. In this figure, the angle
56 is known as the transmission angle and it should preferably be as close to 090 as
possible.
Fig. 21 – Balance of Moments on the SwingJaw
5F
6T
5O
6O
56
39
It should be evident from Figs. 18 and 21 that:
6566 cos FF (11)
From equations (8) and (10), it follows that:
45
5634636
sin
sinsin
rFT (12)
A relationship between 6T and 2T can be obtained from equations (4) and (12), as follows:
4532
5634
62
26
sinsin
sinsin
rT
rT (13)
Equation (12) is in dimensionless form. For a given crusher mechanism, values of 2 , 3 , 4 ,
5 and 6 can be determined from purely kinematical considerations and then the value of the
right-hand side of equation (13) can be determined.
4.4) Application and Discussion of the Results of the Static Force Analysis.
With the data given in Table 2 for the crusher mechanism, given the values of 2 , the
corresponding values of 3 , 4 , 5 and 6 were computed and then used in equation (13) to
determine the corresponding force transmission ratios. The results are plotted in Fig. 22, below.
-200
-150
-100
-50
0
50
100
150
200
0 30 60 90 120 150 180 210 240 270 300 330 360
Anglular Position of the Crank (degrees)
Fo
rce T
ransm
issi
on R
atio
(dim
ensi
onle
ss)
Fig. 22 – Variation of Normalized Torque Ratio with Crank Angle 2 .
40
The first spike in Fig. 22 indicates the great amplification of the crushing force that occurs at the
toggle position, which corresponds to a crank angle of about0180 . Theoretically, the crushing
force amplification should be infinite at this toggle position. The second spike in Fig. 22 occurs
at a crank angle of about0360 . This spike corresponds to the second toggle position of the
mechanism. However, as the crank rotates from 0
2 0 to0
2 180 , the crusher would be on
the idle stroke with the swing jaw being retracted and no work being done in crushing the feed
material.
41
CHAPTER FIVE
5.0) Discussion
5.1) Basis for Selecting a Suitable Crusher Mechanism.
In this chapter, a comparison between the single-toggle, double-toggle and horizontal pitman jaw
crusher mechanisms will be conducted and thereafter a suitable mechanism for a small-scale
mechanized jaw crusher selected.
In order to select the correct machine for any application there are a number of parameters that
must be considered so as to end up with the best machine for the job. Failure to select the correct
machine is often the greatest cause of unsatisfactory performance, and of major production and
maintenance problems.
When selecting a jaw crusher, consideration should be given to the following points:
Maximum feed size should be no greater than 80% of the gape (smaller dimension of the
feed opening).
The operating setting of the crusher (closed side setting) is the smallest dimension
between the fixed jaw plate and the moving jaw plate, measured plate to plate (flat jaws)
or tip to valley (ribbed or corrugated jaws).
Maximum product size will generally be about 1.5 times the closed side setting of the
machine. However, if the feed is a particularly slabby material this may not be the case.
After crushing, 50 – 60% of the product will pass the closed side setting.
Reduction ratios of jaw crushers are generally around 6:1.
The primary crusher should be selected to exceed the average capacity of the plant, as
primary feed to a plant is generally of a cyclical nature, relying on trucks or loaders in
most cases.
Jaw crushers operate at their maximum efficiency when all feed smaller than the closed
side setting is removed to bypass the jaw crusher.
Jaw crushers should be selected on maximum feed size and not the required capacity.
Putting too fine a feed into a jaw crusher will overload the machine, leading to possible
equipment failure.
Type of rock to be crushed (hardness, abrasiveness, bulk density)
Power and/or space limitations.
These factors together with the product size required determine the best crusher for the
application. This selection narrows down to the primary crushers whose actual capacities vary
depending on material hardness, feed grading, moisture content, bulk density, and many other
factors, including the actual installation and method of operation of the machine.
42
Crusher selection can also be based on reduction ratios. The reduction ratio is broadly defined as
the ratio of the feed size to the product size in any crushing operation. It is very useful in
determining what a crusher can do, or is doing, in the way of size reduction. It can also be used
as a partial indicator of the stresses the crusher will be subjected to during operation, an element
in determining the crusher capacity and as an indicator in crusher efficiency. However, there is
no one method of calculation which provides a useful figure for all of these considerations but
instead there are various types of reduction ratios in use;
The limiting reduction ratio which is the ratio of the maximum feed to the maximum product
size. It is the ratio normally understood when reduction ratio is discussed without defining it
further. This figure may vary, especially for the primary crusher feed, because the maximum
feed size for primaries is normally the expected lump in one direction from a blast or passing
through a grizzly, whereas product is generally sized on a square or round mesh, which measures
intermediate dimensions of a particle.
The 80% reduction ratio which is the ratio of the theoretical square mesh aperture that will pass
80% of the feed and 80% of the product was originally derived to eliminate the problems caused
by the presence of a small proportion of coarse slabs of material when using the limiting
reduction ratio in calculations. This is probably the best ratio to use when sizing a crusher or
determining the performance of an existing installation.
These ratios are the most commonly referred to when selecting a suitable machine for an
application. The table below shows the average reduction ratios that apply to the most popular
types of crushers in use in quarries today. It should be noted that these are averages, and specific
machines may achieve better or worse reduction ratios depending on design and application.
43
Table 7: Reduction ratios of different types of crushers
Type of Crusher Reduction Ratio
Single or Double-Toggle jaw crusher 6:1
Gyratory crusher 8:1
Standard head cone crusher 7:1
Fine (short) head cone crusher 5:1
Hammermill or Impactor Up to 10:1
Therefore, a crusher mechanism that will be selected needs to have a reduction ratio that will
perform to the requirements of the design or the customer.
With regards to the three crushing mechanisms that are being considered in this paper, the
horizontal pitman jaw crusher has been phased out in most quarries due to its limited ability to
crush hard materials at economical rates due to inefficient transfer of crushing forces to the jaw
plates.
A comparison between the single-toggle and double-toggle jaw crushers reveals that the double-
toggle design is more complex as well as consisting of more parts thereby making it heavier than
the simply designed single-toggle jaw crusher. This in effect implies that the double toggle
would be more demanding in term of its servicing due to the many parts that constitute the
machine as well as make it expensive to operate and to buy from the manufacturer. The double-
toggle, with its direct reciprocating action of the swing jaw would translate into less energy
wasted during the crushing operation as well as less wear to the crushing jaw plates and would
render it more favorable than the single-toggle. However, despite the elliptical motion of the
single-toggle’s swing jaw translating into a shorter jaw plate life when compared to an equivalent
double-toggle machine, but improvements in jaw plate technology, including the design of
reversible jaw plates, have largely negated this advantage. It has also been found that the
combined grinding and compression action of the single-toggle machine enhances the crushing
capability. The single-toggle machine as a primary crusher has the advantages of having a major
44
cost, weight and size advantage over equivalent double toggle machines and generally requires
less motor power. However, double toggle crushers still have their place, particularly in very
hard and/or abrasive materials.
Why a Single Toggle Jaw Crusher?
Utilization as Primary Crusher in Mines.
High Power & Capacity in Material Crushing.
Manufacture of Friction Resisting Parts from Manganese Steel.
Less Friction & More Resistance Compared to Other Crushers.
Firm Structure & High Resistance.
High Efficiency & Reduction of Preservation Cost via Lubricating Mechanism.
Quick & Easy Exchange of Parts.
5.2) Torque Transmission Characteristics for Different Jaw Crushers
Static force analysis for the double-toggle mechanism was meant to highlight torque and
subsequent force characteristics of the system and their effects on the links of the mechanism,
further material selection process is possible once both static and dynamic characteristics of the
mechanism have been exhaustively studied and analyzed.
In this presentation we start with the input, in which for this case is the angular velocity which is
used to compute other parameters during the analysis. The choice of speed depends on the load
handled by the machine, for hard materials lower speeds are chosen and vice versa, the other
aspect in consideration is inertia force which contributes immensely in the working principle of
the machine, just to mention the flywheel which serves to store energy and even out motion, is at
the same time used as a pulley connected to the prime mover by use of belts.
The criteria used in order to make a comparison of this presentation compared with other toggle
mechanisms, is the torque ratio which serves to highlight transmission of forces to the crushing
chamber, the torque required to crush the load is again determined by the nature of the material
being crushed.
45
We begin with analyzing torque ratios for the double-toggle and then compare with those of
other mechanisms so as to have a clear comparison on the force transmitted and power
consumption.
For the double-toggle, the first spike occurs at and T6/T2 is 5114.04 while the second
spike occurs at and T6r2/T2r6 is 5318.60. The equation used to compute the above values is
expressed as:
4532
5634
62
26
sinsin
sinsin
rT
rT
For the horizontal pitman mechanism, we consider the graphical representation of the torque
ratio, and note the behavior of the links at key angles as shown below:
-650
-500
-350
-200
-50
100
250
400
0 30 60 90 120 150 180 210 240 270 300 330 360
Angular Position of the Crank in Degrees
No
rma
lize
d T
orq
ue
Ra
tio
Fig. 23 – Variation of Normalized Torque Ratio with Crank Angle 2 .
Source: Prof. M.F Oduori (University of Nairobi)
From figure 23, the first spike occurs at 0
2 73 and T4/T2 is 28,029.17 while the second
spike occurs at 0
2 252 and T4/T2 is – 46,564.58. However, as the crank rotates from
46
02 73 to
02 252 , the crusher would be on the idle stroke with the swing jaw being
retracted and no work being done in crushing the feed material. Therefore, the second spike has
no physical meaning in so far as crushing of the feed material is concerned.
The expression used to compute the values is:
23
34
42
24
sin
sin
rT
rT
The above equation is the same as for the double-toggle but the second part of the equation is
omitted; the expression only gives the ratio of the first link and omits the second part involving
the pitman, meaning the losses incurred by the double-toggle have been eliminated.
The previous project for the year 2014 final year Mechanical Engineering students, project code
MFO 02/2014, on “Kinematic and static force transmission analysis of a single-toggle jaw
crusher’’ , the static force analysis carried out resulted in the following expression for the torque
ratio;
32
3
32
23
sin
2sin
rT
rT
The graphical representation of the torque ratio is shown in figure 24.
47
Fig 24. torque ratio T3/T2 for the single toggle Jaw Crusher
Source Code MFO 02/2014
From the graph, the first spike occurs at and T3/T2 is -719.71, while the second spike occurs
at and T3/T2 is 774.96. The values for the torque ratios for a single-toggle mechanism are
relatively low compared to those of the previous mechanisms.
From the above analysis it is clear that the horizontal pitman mechanism has the highest torque
ratios followed by the double-toggle mechanism and lastly the single-toggle mechanism.
Therefore, by purely comparing the mechanisms from a static force transmission point of view,
the horizontal pitman would be the most suitable mechanism followed by the double-toggle and
lastly the single-toggle mechanism. However, the mechanism to be chosen for the design of a
small-scale mechanized stone crusher has to factor in other considerations as described earlier in
this chapter regarding the selection of a suitable crusher mechanism. Hence, despite the single-
toggle having the lowest torque ratios it is still best suited for application in the design of the
small-scale mechanized stone crusher as it has many other advantages over the rest of the
mechanisms.
48
5.3) Conclusion
Single-toggle jaw crushers have an edge over other mechanisms due to high throughput capacity,
simple construction, low space requirement, relatively low weight, efficient transfer of crushing
forces to the jaw plates and lower power consumption.
Therefore, for the design of a small-scale mechanized stone crusher, the single-toggle
mechanism has been found to be the most suitable one for this application.
5.4) Recommendations
With regards to the weight of the crusher itself, there is a need to keep its weight as low
as possible without compromising its performance. This in effect will ensure that the
manufacturing as well as operating costs (to some extent) are significantly reduced.
The moving parts of the crusher need constant lubrication for peak performance of the
crusher.
Use of high strength materials for the jaw plate inserts is recommended to enable the
crushing of hard rocks without excessive wear of the plates and also enabling them to be
replaced when they are worn out.
49
5.5) Further Scope of Study
The equations derived in this paper can be used to investigate the effects of any alterations in the
design of the crusher mechanism, upon its kinematics. Further, given the kinematical equations,
a dynamic force analysis of the mechanism can be carried out to determine variation of stresses
in the links and overall dynamic behaviour of the mechanism. An understanding of the force
transmission characteristics and the dynamic behaviour of the mechanism is essential for sound
design of the crusher.
Further vibrations arising from torque transmission can be studied and design altered to
minimize propagation of the vibrations to adjacent equipments as a safety measure.
50
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