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Procedia CIRP
CIRP 00
00 (2020)
(2020) 000–000
000–000
Procedia
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ScienceDirect
www.elsevier.com/locate/procedia
www.elsevier.com/locate/procedia
Procedia CIRP
00 (2017)
000–000
Procedia
CIRP 91
(2020) 858–863
www.elsevier.com/locate/procedia
30th CIRP Design 2020 (CIRP Design 2020)
Design
ofDesign
a small-scale
stone
crusher
28th CIRP
Conference,granite
May 2018,
Nantes,
France
Tauyanashe
Chikuku ,to
Royanalyze
N. Mushonga
*,
Tendai Sakala
, Wilson
R. Nyemba
, Simon of
A new
methodology
the
functional
and
physical
architecture
a,c
Chinguwaa,c
existing products
for an
assembly
oriented
product
family
identification
Department of
of Mechanical
Mechanical Engineering,
Engineering, University
University of
of Zimbabwe,
Zimbabwe, P
PO
O Box
Box MP
MP 167,
167, Mount
Mount Pleasant,
Pleasant, Harare,
Harare, Zimbabwe
Zimbabwe
Department
aa
a,
a,
aa
a,b
a,b
aa
bb
Department
Department of
of Quality
Quality and
and Operations
Operations Management,
Management, Faculty
Faculty of
of Engineering
Engineering and
and the
the Built
Built Environment,
Environment, University
University of
of Johannesburg,
Johannesburg, Auckland
Auckland Park
Park Bunting
Bunting
Road
Road Campus,
Campus, South
South Africa.
Africa.
cc
Department of
of Mechanical
Mechanical Engineering
Engineering Science,
Science, Faculty
Faculty of
of Engineering
Engineering and
and the
the Built
Built Environment,
Environment, University
University of
of Johannesburg,
Johannesburg, Auckland
Auckland Park
Park Kingsway
Kingsway
Department
Campus,
Campus, Auckand
Auckand Park
Park 2006,
2006, Johannesburg,
Johannesburg, South
South Africa.
Africa.
Paul Stief *, Jean-Yves Dantan, Alain Etienne, Ali Siadat
École Nationale Supérieure d’Arts et Métiers, Arts et Métiers ParisTech, LCFC EA 4495, 4 Rue Augustin Fresnel, Metz 57078, France
* Corresponding
Corresponding author.
author. Tel.:
Tel.: +263713900710;
+263713900710; fax:
fax: +263-242-303280.
+263-242-303280. E-mail
E-mail address:
address: nyasharoy@gmail.com
nyasharoy@gmail.com
*
* Corresponding author. Tel.: +33 3 87 37 54 30; E-mail address: paul.stief@ensam.eu
Abstract
Abstract
Abstract
This paper
paper describes
describes the
the design
design of
of aa manually
manually operated
operated granite
granite stone
stone crushing
crushing machine.
machine. This
This machine
machine is
is targeted
targeted for
for people
people who
who are
are currently
currently in
in
This
the
the stone
stone crushing
crushing business
business and
and use
use manual
manual methods
methods like
like the
the hammer
hammer and
and anvil.
anvil. Due
Due to
to the
the expensive
expensive nature
nature of
of available
available stone
stone crushers
crushers in
in
In today’s
business
environment,
trend people
towards
moreafford
product
variety
andand
customization
unbroken.ways
Dueof
this development,
need of
Zimbabwe
small-scale
crushingthe
business
people
cannot
afford
these
machines
and
hence resort
resort is
to primitive
primitive
ways
oftocrushing
crushing
that are
are both
both the
tedious
Zimbabwe
small-scale
crushing
business
cannot
these
machines
hence
to
that
tedious
harmful.
After
analysis
of
stone
crushing
and
thorough
aa solution
was
that
safe,
agile and
andpotentially
reconfigurable
production
systems
emerged
to cope
with
variousmethods
products
productstudy,
families.
To design
and optimize
production
and
potentially
harmful.
After careful
careful
analysis
of current
current
stone
crushing
methods
andand
thorough
study,
solution
was developed
developed
that is
is
safe,
affordable
solution
addresses
the
of
stone
provides
Research
systems
as welland
as efficient.
to chooseThe
thedeveloped
optimal product
methods
are crushers
needed. and
Indeed,
mostaa viable
of the alternative.
known methods
aim to
affordable
and
efficient.
The
developed
solution matches,
addresses product
the needs
needsanalysis
of the
the hammer
hammer
stone
crushers
and
provides
viable
alternative.
Research
wasa performed
performed
through
experiments,
thethe
usephysical
of local
local level.
libraries
and site
siteproduct
visits to
to families,
stone crushing
crushing
companies
and various
various
quarry
sites
thatnumber
use the
the and
analyze
product orthrough
one product
family on
Different
however,
may differ
largely quarry
in terms
of the
was
experiments,
the
use
of
libraries
and
visits
stone
companies
and
sites
that
use
and
were
conduct
experiments
and
minimum
crushing
needed
for
hammer
and anvil
anvil approach.
approach.
University
laboratories
were used
used to
toand
conduct
experiments
and determine
determine
minimum
crushing forces
forces
needed
for
naturehammer
of components.
This fact University
impedes anlaboratories
efficient comparison
choice
of appropriate
product family
combinations
for the
production
various
granite
stones.
A
portable
stone
crushing
machine
was
then
designed
which
meets
the
minimum
crushing
force
of
225KN.
An
additional
various
granite
stones.
A
portable
stone
crushing
machine
was
then
designed
which
meets
the
minimum
crushing
force
of
225KN.
An
additional
system. A new methodology is proposed to analyze existing products in view of their functional and physical architecture. The aim is to cluster
of
10%
to
safety
the
and
potential
to
stones
range
of
granite
stone.
granite
allowance
of new
10% assembly
to carter
carter for
for
safety of
of
the machine
machine
andfor
potential
to crush
crush other
other
stones within
within
rangelines
of the
theand
granite
stone. The
The
small
scale
granite
theseallowance
products in
oriented
product
families
the optimization
of existing
assembly
the creation
ofsmall
futurescale
reconfigurable
stone crusher
crusher was
was designed
designed to
to crush
crush stones
stones of
of approximately
approximately 25-135mm
25-135mm to
to about
about 24-20.2mm
24-20.2mm in
in size.
size. SOLID
SOLID WORKS
WORKS was
was used
used as
as aa stress
stress
stone
assembly systems. Based on Datum Flow Chain, the physical structure of the products is analyzed. Functional subassemblies are identified,
and
analysis tool
tool on
on the
the gear
gear (main
(main crushing
crushing part)
part) to
to determine
determine the
the regions
regions where
where the
the gear
gear experiences
experiences maximum
maximum force
force according
according to
to Von-Misses
Von-Misses
analysis
a functional analysis is performed. Moreover, a hybrid functional and physical architecture graph (HyFPAG) is the output which depicts the
failure
criteria.
was
the
inner
diameter
of
assembly
and
gears
are prone
high
stress
results
in
failurebetween
criteria. It
Itproduct
was observed
observed
theby
inner
diameterdesign
of the
the gear
gear
assembly
and the
the
gears themselves
themselves
prone to
to
high
stress which
which
resultsAn
in tearing
tearing
similarity
families
providing
support
to both,
production
system are
planners
and
product
designers.
illustrative
off of
of the
the material
material in
in those
those regions.
regions.
off
example of a nail-clipper is used to explain the proposed methodology. An industrial case study on two product families of steering columns of
thyssenkrupp
Presta
France
is then carried
out B.V.
to B.V.
give a first industrial evaluation of the proposed approach.
©
2020 The
The
Authors.
Published
Elsevier
2020
The
Authors.
Published
byby
Elsevier
© 2020
Authors.
Published
by
Elsevier
B.V.
© 2017
The
Authors.
Published
byunder
Elsevier
B.V.
This
is
an
open
access
article
the
CC
BY-NC-ND
(http://creativecommons.org/licenses/by-nc-nd/4.0/)
Peer-review
under
responsibility
of
the
scientific
of
Design
Peer-review under responsibility of the scientific committee
committeelicense
of the
the CIRP
CIRP
Design Conference
Conference..
Peer-review
underunder
responsibility
of theofscientific
committee
of theof28th
CIRPBioManufacturing
Design ConferenceConference
2018.
Peer-review
responsibility
the scientific
committee
the CIRP
2019.
Keywords: Granite
Granite stone
stone crusher;
crusher; crushing
crushing force;
force; quarry
quarry stones.
stones.
Keywords:
Keywords: Assembly; Design method; Family identification
1. Introduction
Introduction
1.
As indicated
indicated in
in Fig.
Fig. 1,
1, the
the crushing
crushing process
process involves
involves
As
transferring
force
which
can be
be amplified
amplified
by mechanical
mechanical
of
the product
rangewhich
and characteristics
manufactured
and/or
transferring
aa force
can
by
advantage
aa material
that
has
bonds
with
This
advantage through
through
material
that context,
has stronger
stronger
bondschallenge
with aa in
This paper
paper provides
provides aa problem
problem solver
solver for
for aa small-scale
small-scale stone
stone
assembled
in this system.
In this
the main
higher
to
compared
to
being
crushing
in
not
crushing
higher resist
resistand
to deformation
deformation
as
compared
to the
the
material
being
crushing
industry
in Zimbabwe,
Zimbabwe,
not only
only
making
stone
crushing
Due
to industry
the fast
development
inmaking
the stone
domain
of
modelling
analysis is as
now
not only
to material
cope with
single
crushed.
Crushing
devices
hold
material
between
two
parallel
easier
and
more
productive
but
also
making
it
more
desirable
crushed. Crushing
hold
material
betweenproduct
two parallel
easier and more
but also
making
it more desirable
communication
andproductive
an ongoing
trend
of digitization
and
products,
a limiteddevices
product
range
or existing
families,
or tangent
tangent solid
surfaces, and
and apply
apply sufficient
sufficient force
force to
to bring
bring the
career choice
choice
for those
those who
whoenterprises
were limited
limited
by
risk of
ofimportant
injury or
or
or
surfaces,
career
for
were
risk
injury
digitalization,
manufacturing
areby
facing
but
also tosolid
be able
to analyze
and to
compare
products
to the
define
surfaces together
together to
to generate
generate enough
enough energy
energy within
within the
the material
material
low body
body strength.
strength. Stone
Stone crushing
crushing is
is reducing
reducing the
the size
size of
of large
large
surfaces
low
challenges in today’s market environments: a continuing
new product families. It can be observed that classical existing
being
so
that
its
separate
or
change
rocks
into
rocks
or
Quarry
in this
being crushed
crushed
so are
thatregrouped
its molecules
molecules
separateoffrom,
from,
or or
change
rocks towards
into smaller
smaller
rocks or
orofgravel
gravel
or dust.
dust.
Quarry stones
stones
this
tendency
reduction
product
development
timesinand
product
families
in function
clients
features.
alignment
in
relation
to,
each
other
[2].
However,
paper
refer
to
granite
¾
inches
(20mm)
or
less.
These
stones
are
alignment in relation to, each other [2]. However, the
the
paper refer to granite ¾ inches (20mm) or less. These stones are
shortened
product
lifecycles.
In
addition,
there
is
an
increasing
However,
assembly
oriented
product
families
are
hardly
to
find.
vital
convectional way
way of
of stone
stone crushing
crushing consists
consists of
of high
high chances
chances of
of
vital to
to the
the construction
construction industry
industry and
and when
when crushed
crushed are
are mainly
mainly convectional
demand
of
customization,
being
at
the
same
time
in
a
global
On
the
product
family
level,
products
differ
mainly
in
self-inflicted injuries
injuries such
such as
as injuring
injuring fingers
fingers when
when holding
holding the
the two
used for
for road
road base
base aggregate
aggregate and
and in
in concrete
concrete mix
mix [1].
[1].
self-inflicted
used
competition with competitors all over the world. This trend,
main characteristics: (i) the number of components and (ii) the
which
is inducing
the
development
to micro
type of components (e.g. mechanical, electrical, electronical).
2212-8271
© 2020
2020 The
The
Authors.
Published by
by from
Elsevier macro
B.V.
2212-8271
©
Authors.
Published
Elsevier
B.V.
markets,
results
in
diminished
lot
sizes
due
to
augmenting
Classical
Peer-review
under
responsibility
of
the
scientific
committee
of
the
CIRP
Design
Conference
2020.
Peer-review under responsibility of the scientific committee of the CIRP Design Conference
2020. methodologies considering mainly single products
product varieties (high-volume to low-volume production) [1].
or solitary, already existing product families analyze the
To cope with this augmenting variety as well as to be able to
product structure on a physical level (components level) which
identify possible optimization potentials in the existing
causes difficulties regarding an efficient definition and
production system, it is important to have a precise knowledge
comparison of different product families. Addressing this
1. Introduction
2212-8271 © 2020 The Authors. Published by Elsevier B.V.
This is an©open
article Published
under theby
CC
BY-NC-ND
2212-8271
2017access
The Authors.
Elsevier
B.V. license (http://creativecommons.org/licenses/by-nc-nd/4.0/)
Peer-review
under
responsibility
of scientific
the scientific
committee
theCIRP
CIRP
BioManufacturing
Conference 2019
Peer-review
under
responsibility
of the
committee
of the of
28th
Design
Conference 2018.
10.1016/j.procir.2020.03.119
Tauyanashe Chikuku et al. / Procedia CIRP 91 (2020) 858–863
2
Chikuku et al./ Procedia CIRP 00 (2020) 000–000
rocks and eyes due to flying stones during impact. Not only is
this unsafe to the person at hand but also to the people around.
As a result, there was a need to design a machine that is more
efficient, secure and environmental friendly during operation.
As part of the research, interviews were conducted so as to get
a better understanding of the working environment. General
questions asked such as:
•What are the challenges faced in using the hammer and
anvil method?
•What is the rate of production?
•What are the general needs/requirements on machine to be
designed?
Fig. 1. Basic Principles of rock crushing [2]
Some of the responds given were:
Safety is a prime concern as one has to be very careful
otherwise one can lose a hand, there is also risk of inhalation of
quarry dust. Some hammer and anvil crushers have also tried to
find alternative methods but generally the cost of the machines
is very high and also the cost of maintenance is not worth it.
There is also the problem of getting a power source on site.
Because the hammer and anvil method is slow, the crushers
cannot meet high demand of crushed rock and they lose
customers to bigger companies due to inadequate amount of
rock available as the customer would have to wait for days for
enough crushed stone to be gathered. Average time taken to fill
one-wheel barrow with crushed granite is 1hr 30mins that is not
including time taken to retrieve stone from the dwalas and
breaking them into manageable sizes. The cost of one cubic
metre of crushed stone is USD$24 and 1 cubic is equal to 12
wheelbarrows of stone. Sorting of stone to desired sizes is a
major setback.
The information obtained tallies with the main aims of the
designing a machine that provides better working conditions
and safer environment.
special qualifications and hence many people have resorted to
it for a living. There is also a high demand in construction
materials like quarry stones due to the increase in the number
of housing cooperatives in recent years. These stone crushers
obtain their granite rock from local dwalas by exposing the
parent rock (dwala) to extreme fluctuating temperatures
through the burning of tires over the dwalas (Fig. 2). After
cooling, pieces of rock can be chipped off using a sledge
hammers, the process is basically forced exfoliation. These
chunks of rock are then crushed into the desired aggregates to
be sold for their various application.
Fig. 2. Setting up tyre to burn Dwala
Rock crushers are used for breaking rock particles into
smaller fragments. Rock materials of different sizes, normally
called aggregates, are used as building materials in a vast
number of products and applications in modern society.
Infrastructure and building industries are heavily dependent on
rock material with specified characteristics as the basis for
foundations, concrete structures, roads and so on. Hence this
gives a strong incentive to facilitate the production of
aggregates at low cost, high quality and low environmental
footprint [3].
3. Previous designs
Fig. 3. presents a manual stone crusher which was designed
by New Dawn Engineering (Swaziland). The main
disadvantage of this crusher is that it is not locally available and
has poor safety mechanisms incase an uncrushable material
enter the crusher. The new Dawn crusher is also operated by at
least five individuals and it is said to be able to produce 10 cubic
metres of stone per day.
2. Background
The small-scale (hammer and anvil) stone crushing sector is
an important part of the stone crushing industry, it is not
necessarily new but it is growing by the day along with the
slight boom in construction that can be attributed to the increase
in the number of housing cooperatives and similar schemes.
The closing of major companies in Zimbabwe has resulted in
high unemployment rate and this has resulted in people relying
on informal work like stone crushing. This work requires no
Fig. 3. New Dawn Engineering manual stone crusher [4]
859
3
Chikuku et al./
Procedia
CIRP
00 (2020)CIRP
000–000
Tauyanashe
Chikuku
et al.
/ Procedia
91 (2020) 858–863
860
Another type of manual stone crusher is the crazy crusher; it
is mainly used in laboratories for crushing rock samples for
testing. It uses a lever to create the necessary force needed to
crush stone. Currently its design is still patent pending. The
crazy crusher is very small and therefore would not work for
big quantities of rock. it also crushes stone into fine powder
which is not ideal as the desired level of crushing in this case is
¾ inches.
Fig. 5. Open ended steel cylinder, plunger, base plate.
Fig. 4. Crazy crusher
4. Methodology
4.1. Experimental results
In order to come up with the design, experimental work was
carried out to determine parameters such as the minimum force
required to start crushing, size of the aggregate obtained at
different loads. By considering the aggregate crushing value
(ACV) which gives a relative measure of the resistance of an
aggregate to crushing under a gradually applied compressive
load. It was observed that they was a gradual decrease in ACV
as the aggregates decreased in size. The standard aggregate
crushing test shall be made an aggregate passing the 24mm BS
test sieve and retained on the 20.2mm BS test sieve.
4.2. Apparatus
The following apparatus is required for the standard test.
•An open-ended steel cylinder of nominal 150mm internal
diameter, with a plunger and a baseplate
•A straight steel tamping rod, of circular cross-section
16mm diameter, and 450mm to 600mm long, rounded at the
end
•A balance 3000g accurate to 1 g
•BS sieves, sizes 24mm; 20.2mm;
•A compression testing machine, capable of applying force
of 400kN at a uniform rate so that maximum load is reached in
10mins.
•A rigid cylindrical metal measure, for measuring the
sample, of internal diameter 115mm and an internal depth of
180mm
Fig. 6. Final sieved aggregate on scale.
The granite was put under gradual load and it was observed
that 225KN was the minimum load under which the granite was
crushed to 20.2 mm.
Impact force required is 400N
Average force from a human arm is 150N
Average force from pedalling used as 200N
The relationship between the impact force required (400N)
and the average force of a human (150-200N) shows that
without mechanical advantage it would be near impossible to
crush granite. Therefore, the aim for the success is for the
machine to offer at least double the mechanical advantage that
is to ensure crushing will occur.
5. Governing equations
According to Chakrabarty [8] The constitutive equations of
the elastic-plastic deformation of a material is based on
combining the Hooke’s law and either the Incremental or
Deformation theory which are stated as below.
According to Hooke’s law:
�
𝑑𝑑𝑑𝑑��
=�
1 + 𝑣𝑣
1 − 2𝑣𝑣
� 𝑠𝑠̇�� + �
� 𝜎𝜎̇�� 𝛿𝛿��
𝐸𝐸
3𝐸𝐸
Based on Prandtl-Reuss Incremental Theory (IT):
(1)
Tauyanashe Chikuku et al. / Procedia CIRP 91 (2020) 858–863
4
1 − 2𝑣𝑣
� 𝜎𝜎̇�� 𝛿𝛿��
3
3𝜎𝜎�̇ 𝐸𝐸
+
� − 1� 𝑠𝑠��
2𝜎𝜎� 𝐸𝐸�
𝐸𝐸𝜀𝜀̇�� = (1 + 𝑣𝑣)𝑠𝑠̇�� + �
3
𝐸𝐸� 2𝑞𝑞 − 𝑝𝑝 𝑠𝑠
𝑐𝑐�� = �1 − � �
�
𝐸𝐸�
𝜎𝜎�
𝜎𝜎�
2
(2)
𝑐𝑐�� = 3
According to the Deformation theory (DT):
𝐸𝐸𝜀𝜀̇�� = �
861
Chikuku et al./ Procedia CIRP 00 (2020) 000–000
3𝐸𝐸 1 − 2𝑣𝑣
1 − 2𝑣𝑣
+
� 𝑠𝑠̇�� + �
� 𝜎𝜎̇�� 𝛿𝛿��
2𝐸𝐸�
2
3
3𝜎𝜎�̇ 𝐸𝐸 𝐸𝐸
+
� − � 𝑠𝑠
2𝜎𝜎� 𝐸𝐸� 𝐸𝐸� ��
(3)
Where:
𝜀𝜀̇�� is the change in strain and 𝑖𝑖 𝑎𝑎𝑎𝑎𝑎𝑎 𝑗𝑗 = 1,2 or 3
𝜎𝜎̇�� is the change in stress
𝜎𝜎�̇ is the change in the effective stress
𝑣𝑣 poison ratio
𝐸𝐸� is tangent modulus
𝐸𝐸� = 𝜎𝜎� ⁄𝜀𝜀̅
𝑠𝑠̇�� is the stress deviator tensor given by:
𝐼𝐼
𝑠𝑠�� = 𝜎𝜎�� − 𝛿𝛿��
3
By further manipulating the above equation, the stress rate
corresponding to the strain rate in the can be expressed as:
𝜎𝜎̇�
𝛼𝛼 𝛽𝛽 𝒳𝒳 𝜀𝜀̇�
(4)
� 𝜎𝜎̇� � = 𝐸𝐸 � 𝛽𝛽 𝛾𝛾 𝜇𝜇 � � 𝜀𝜀̇� �
𝜏𝜏̇ ��
𝒳𝒳 𝜇𝜇 𝛿𝛿 𝛾𝛾̇��
Where The corresponding parameters 𝛼𝛼, 𝛽𝛽, 𝛾𝛾, 𝛿𝛿, 𝜇𝜇, 𝒳𝒳 depend on the type of
plasticity theory used i.e. IT or DT and 𝐸𝐸 is the Young modulus.
1
� )
(𝑐𝑐 𝑐𝑐 − 𝑐𝑐��
𝜌𝜌 �� ��
1
𝛽𝛽 = (𝑐𝑐�� 𝑐𝑐�� − 𝑐𝑐�� 𝑐𝑐�� )
𝜌𝜌
1
� )
𝛾𝛾 = (𝑐𝑐�� 𝑐𝑐�� − 𝑐𝑐��
𝜌𝜌
1
𝒳𝒳 = (𝑐𝑐�� 𝑐𝑐�� − 𝑐𝑐�� 𝑐𝑐�� )
𝜌𝜌
1
𝜇𝜇 = (𝑐𝑐�� 𝑐𝑐�� − 𝑐𝑐�� 𝑐𝑐�� )
𝜌𝜌
1
� )
𝛿𝛿 = (𝑐𝑐�� 𝑐𝑐�� − 𝑐𝑐��
𝜌𝜌
𝑐𝑐
𝑐𝑐
𝑐𝑐
𝐸𝐸 �� �� ��
𝜌𝜌 = �𝑐𝑐�� 𝑐𝑐�� 𝑐𝑐�� �
𝐸𝐸� 𝑐𝑐
�� 𝑐𝑐�� 𝑐𝑐��
𝛼𝛼 =
(5a)
(5b)
(5c)
(5d)
(5e)
(5f)
(5g)
𝐸𝐸�
𝑞𝑞�
𝑠𝑠 �
� � � + ��
𝐸𝐸� 4𝜎𝜎�
𝜎𝜎�
1
𝐸𝐸�
𝑐𝑐�� = − �1 − (1 − 2𝑣𝑣)
2
𝐸𝐸
𝐸𝐸�
𝑝𝑝𝑝𝑝
𝑠𝑠 �
− 3 �1 − � � � + � ��
𝐸𝐸� 2𝜎𝜎�
𝜎𝜎�
3
𝐸𝐸� 2𝑝𝑝 − 𝑞𝑞 𝑠𝑠
𝑐𝑐�� = �1 − � �
�
𝐸𝐸�
𝜎𝜎�
𝜎𝜎�
2
𝐸𝐸�
𝑝𝑝�
𝑠𝑠 �
𝑐𝑐�� = 1 − 3 �1 − � � � + � �
𝐸𝐸� 4𝜎𝜎�
𝜎𝜎�
(6f)
Let 𝜎𝜎� = −𝑝𝑝, 𝜎𝜎� = −𝑞𝑞, 𝜏𝜏�� = −𝑠𝑠 at the point of bifurcation.
Assuming that the material is in a state of plane stress i.e.
𝜎𝜎� = 𝜏𝜏�� = 𝜏𝜏�� =0, the effective stress 𝜎𝜎� can be expressed
as:
�
(7)
𝜎𝜎� � = 𝜎𝜎�� − 𝜎𝜎� 𝜎𝜎� + 𝜎𝜎�� + 3𝜏𝜏��
G. H. Handelman and W. Prager [10] carried out serval
experiments focusing on the plastic deformation analysis of a
material (plate under compressive load) in order to assess the
difference between the IT and DT. They observed that their
results obtained by DT were in good agreement with the
experimental results. Based on studies carried out by
Handelman the present study only focused on using DT.
The basic integral of uniqueness of a material under
deformation is given by the strain energy function given by
Chakrabarty [8] as:
1
(8)
��𝜎𝜎̇� 𝜀𝜀̇� + 𝜎𝜎̇� 𝜀𝜀̇� + 𝜏𝜏̇�� 𝛾𝛾̇�� �𝑑𝑑𝑑𝑑
2
The potential energy V for the material subjected to uniform
in-plane compressive stresses is given as:
1
𝜕𝜕𝜕𝜕 �
𝜕𝜕𝜕𝜕 �
− � �𝜎𝜎� ℎ � � + 𝜎𝜎� ℎ � �
2
𝜕𝜕𝜕𝜕
𝜕𝜕𝜕𝜕
(9)
𝜕𝜕𝜕𝜕 𝜕𝜕𝜕𝜕
+ 2𝜏𝜏�� ℎ � � � �� 𝑑𝑑𝑑𝑑
𝜕𝜕𝜕𝜕 𝜕𝜕𝜕𝜕
𝑈𝑈 =
By using calculus of variation, Solid Works is able to use the
Euler-Lagrange differential equations associated with the
minimization of the total potential energy functional with
respect to the arbitrary variation of the displacement function
w, which is given by:
δ(U+V)=0
(10)
The aggregate crushing value is calculated by the following
equation:
Aggregate crushing value % = B/A×100 (11)
According to the deformation theory:
𝑐𝑐�� = 1 − 3 �1 −
𝐸𝐸�
𝐸𝐸�
𝐸𝐸� 𝑠𝑠 �
− (1 − 2𝑣𝑣) + 9 �1 − � �
𝐸𝐸�
𝐸𝐸
𝐸𝐸� 𝜎𝜎�
(6e)
(6a)
(6b)
(6c)
(6d)
Where:
A= mass of surface dry sample
B=the mass of the fraction passing the 2,36mm BS sieve
load is determined by:
L=(14L_1)/(P+4)
(12)
Where:
L = load to give percentage fines within the range 7.5 to
12.5%
L1 = first test load
P = percentage fines obtained with the first load
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862
Chikuku et al./ Procedia CIRP 00 (2020) 000–000
In the case of this design, the flywheel is directly attached to
the crank therefore the input torque is a product of the crank
force and the radius of the flywheel. An average human person
can easily rotate a crank of radius 0.35m with radius of flywheel
0.4m to give allowance to screw on the handle.
The energy stored in a flywheel is calculated by [5]:
∆𝐸𝐸 = 𝑚𝑚𝑅𝑅 � 𝜔𝜔 � 𝐾𝐾�
(13)
Where:
m=mass of flywheel
R=radius of flywheel=0.4m
𝜔𝜔=angular speed of rotation of flywheel
5
bottom of the jaws. The ores are fed to the machine from the
top where the jaws are at the maximum distance 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 particles 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.
The gear diameter was designed considering available space
(0.5m) and the velocity ratio 2:1[5]
𝐷𝐷� + 𝐷𝐷� ≤ 0.5
(14)
Where
𝐷𝐷� =pitch diameter of pinion
𝐷𝐷� =pitch diameter of gear
The jaw of the crusher is responsible for transferring the rotary
motion of the eccentric shaft and applying the reciprocating
motion to the wear plate, therefore it provides the crushing
force of the jaw crusher and hence it is a critical component.
The thickness of the jaw was calculated from equation 5 [5].
𝑀𝑀𝑀𝑀
2𝐼𝐼�
Where:
𝑀𝑀 is the bending moment
𝑡𝑡 is the thickness of the jaw
𝐼𝐼� second moment of inertia
𝜎𝜎� =
Fig. 7 Sketch plan view showing mechanism for the crusher
(15)
6. Design
6.1. Operating and principle in detail
The mechanism of jaw crusher is to crush using impact on
the upper parts of the jaw, with a little shear towards the bottom.
Jaw crushers consist of two jaws. One fixed and the other
reciprocating. The opening between them is largest at the top
(gape) and decreases towards the bottom (set). The jaw moves
on an eccentric shaft and the lower part is hinged on the toggles.
The rock is thrown between two jaws and crushed by
mechanical pressure. Rotational motion 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 gaper size of
the crushed product from the jaw crusher. The rocks are crushed
until they are small enough to pass through the gap at the
Fig. 8. Exposed (a)Side view (b) Plan (c) Isometric view
The flywheels have crank handles as was with the original
design however the flywheel shaft is connected to spur gears
that transfer power to the eccentric shaft thus there are now two
shafts instead of one. The ratio of the gears simply 1:2 so as to
double the torque provided by the human operator. These gears
also further improve the smoothness of operating the crusher,
reducing shock to the operator cranking the mechanism. This is
because the gears have their own mass and hence inertia such
that once they start moving they will tend to resist motion in the
backward direction.
6.2. Stress analysis on the main gear
Fig. 9 indicates a simulation done by Solid Works of the
mild steel gear, stressing out the regions expressing high and
low amounts of stress during crushing. By assuming the gear
will undergo elastic-plastic deformation (deformation theory)
Tauyanashe Chikuku et al. / Procedia CIRP 91 (2020) 858–863
6
Chikuku et al./ Procedia CIRP 00 (2020) 000–000
and according to the Von-Mises failure criteria the gear will
experience maximum stress at the root of the gear with stresses
ranging from 6.767 to 9.473MPa. It was also observed that the
regions surrounding the key way will also experience high
stresses as a results of the high torque and resistance
experienced during crushing.
863
[3] Quist, J, Cone crusher modelling and simulation. Development of a virtual
rock crushing environment based on the discrete element method with
industrial scale experiment validation. Goteborg, Chalmers University of
Technology. 2012.
[4] New Dawn Engineering. (2017). Rock crushing assembly instruction
manual. Swaziland: New Dawn Engineering.
[5] Khurmi R.S, G. J., 2005. A textbook of machine design. 14th ed. New Delhi:
Eurasia Publishing House.
[6] Hurst, K., Concept selection in engineering design Principles. 1999, New
York: John Wiley and Sons, pp. 53-63.
[7] Jones, J., Stone crushing. Complexities of construction, 2012, 1(1), p. 123.
14th ed. 2004, New Delhi: Eurasia Publishing House.
[8]. Chakrabarty. Applied Plasticity,. 2010
[9] Oduori, M., Mutuli, S. and Munyasi, D. , Analysis of the single toggle jaw
crusher kinematics, Journal of Engineering, Design and Technology, 2015,
Vol. 13 No. 2, pp. 213-239.
[10] G. H. Handelman and W. Prager, “Plastic buckling of a rectangular plate
under edge thrusts,” 1949
Fig. 9 Stresses on main gear
7. Conclusions
The purpose of this paper was to design a manually operated
stone crusher that is efficient and affordable so as to suit the
needs of the target market which is small scale stone crushers
that depend on the hammer and anvil method of rock crushing.
From the static and dynamic analysis of the jaw crusher
mechanism it was noted that the jaw crusher can provide up to
60 times the mechanical advantage relating input and output
torque, the use of gears also makes work easier for the operator
of the machine. The combined weight of the machine is up to
200kg, due to heavy components like the flywheels which
weigh 60kgs a piece, the ribbed casing combined with the jaws
and wear plates provide the additional weight in order to
balance the machine. It is thus recommended that the machine
be disassembled in transit and assembled at the crush site, all
components are modular hence assembling the machine is very
simple.
Acknowledgements
The authors wish to acknowledge the assistance from the
construction company, Design Team as well as other small sale
contractors from where the data was collected and eventual
testing of the mortar spraying machine. The researchers would
also want to appreciate the residents of Budiriro in Harare
whose homesteads and construction sites were visited. In
addition, the authors are also grateful for the financial support
provided by the Royal Academy of Engineering to promote
such innovations through conferences and publications.
References
[1] Moavenzadeh, F, Concise encyclopedia of building and Construction
Materials. Masettuses : MIT Press, 1990.
[2]
Satyendra,
2015.
Ispat
Guru.
[Online]
Available
at:
http://ispatguru.com/crushers-and-their-types