Design of a small-scale granite stone crusher PDF

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ScienceDirect Procedia CIRP 91 (2020) 858–863

www.elsevier.com/locate/procedia

30th CIRP Design 2020 (CIRP Design 2020)

Design of a small-scale granite stone crusher Tauyanashe Chikukua, Roy N. Mushongaa,*, Tendai Sakalaa, Wilson R. Nyembaa,b, Simon Chinguwaa,c b

a Department of Mechanical Engineering, University of Zimbabwe, P O Box MP 167, Mount Pleasant, Harare, Zimbabwe Department of Quality and Operations Management, Faculty of Engineering and the Built Environment, University of Johannesburg, Auckland Park Bunting Road Campus, South Africa. c Department of Mechanical Engineering Science, Faculty of Engineering and the Built Environment, University of Johannesburg, Auckland Park Kingsway Campus, Auckand Park 2006, Johannesburg, South Africa.

* Corresponding author. Tel.: +263713900710; fax: +263-242-303280. E-mail address: [email protected]

Abstract This paper describes the design of a manually operated granite stone crushing machine. This machine is targeted for people who are currently in the stone crushing business and use manual methods like the hammer and anvil. Due to the expensive nature of available stone crushers in Zimbabwe small-scale crushing business people cannot afford these machines and hence resort to primitive ways of crushing that are both tedious and potentially harmful. After careful analysis of current stone crushing methods and thorough study, a solution was developed that is safe, affordable and efficient. The developed solution addresses the needs of the hammer stone crushers and provides a viable alternative. Research was performed through experiments, the use of local libraries and site visits to stone crushing companies and various quarry sites that use the hammer and anvil approach. University laboratories were used to conduct experiments and determine minimum crushing forces needed for various granite stones. A portable stone crushing machine was then designed which meets the minimum crushing force of 225KN. An additional allowance of 10% to carter for safety of the machine and potential to crush other stones within range of the granite stone. The small scale granite stone crusher was designed to crush stones of approximately 25-135mm to about 24-20.2mm in size. SOLID WORKS was used as a stress analysis tool on the gear (main crushing part) to determine the regions where the gear experiences maximum force according to Von-Misses failure criteria. It was observed the inner diameter of the gear assembly and the gears themselves are prone to high stress which results in tearing off of the material in those regions.

© 2020 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/) Peer-review under responsibility of the scientific committee of the CIRP BioManufacturing Conference 2019. Keywords: Granite stone crusher; crushing force; quarry stones.

1. Introduction This paper provides a problem solver for a small-scale stone crushing industry in Zimbabwe, not only making stone crushing easier and more productive but also making it more desirable career choice for those who were limited by risk of injury or low body strength. Stone crushing is reducing the size of large rocks into smaller rocks or gravel or dust. Quarry stones in this paper refer to granite ¾ inches (20mm) or less. These stones are vital to the construction industry and when crushed are mainly used for road base aggregate and in concrete mix [1].

As indicated in Fig. 1, the crushing process involves transferring a force which can be amplified by mechanical advantage through a material that has stronger bonds with a higher resist to deformation as compared to the material being crushed. Crushing devices hold material between two parallel or tangent solid surfaces, and apply sufficient force to bring the surfaces together to generate enough energy within the material being crushed so that its molecules separate from, or change alignment in relation to, each other [2]. However, the convectional way of stone crushing consists of high chances of self-inflicted injuries such as injuring fingers when holding the

2212-8271 © 2020 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/) Peer-review under responsibility of the scientific committee of the CIRP BioManufacturing Conference 2019 10.1016/j.procir.2020.03.119

Tauyanashe Chikuku et al. / Procedia CIRP 91 (2020) 858–863

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]

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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.

1 + ฀฀ 1 − 2฀฀ ฀฀฀��� = � � ฀󰇗�� + � �฀฀�� ฀฀�� ฀฀ 3 ฀฀ According to Hooke’s law:

Based on Prandtl-Reuss Incremental Theory (IT):

(1)

Tauyanashe Chikuku et al. / Procedia CIRP 91 (2020) 858–863

1 − 2฀฀ ฀฀฀󰇗�� = (1 + ฀฀)฀฀󰇗�� + � �฀฀󰇗�� ฀฀�� 3 3฀฀ �󰇗 ฀฀ + � − 1�฀฀�� 2฀฀ � ฀฀�

3 ฀฀ 2฀฀− ฀฀ ฀฀ ฀฀�� = �1 − ��� � ฀฀� ฀฀ � ฀฀ � 2

(2)

฀฀�� = 3

According to the Deformation theory (DT):

3฀฀ 1 − 2฀฀ 1 − 2฀฀ ฀฀฀󰇗�� = � + �฀฀�� + � �฀฀󰇗�� ฀฀�� 2 ฀฀� 2 3 3฀฀ �󰇗 ฀฀ ฀฀ + � − �฀฀ 2฀฀ � ฀฀� ฀฀� ��

(3)

Where: ฀฀󰇗�� is the change in strain and ฀฀ ฀฀฀฀฀฀ ฀฀ = 1,2 or 3 ฀฀󰇗�� is the change in stress ฀฀�󰇗 is the change in the effective stress ฀฀ poison ratio ฀฀� is tangent modulus ฀฀� = ฀฀�⁄ ฀฀ ฀฀󰇗�� is the stress deviator tensor given by: ฀฀ ฀฀�� = ฀฀�� − ฀฀�� 3 By further manipulating the above equation, the stress rate corresponding to the strain rate in the can be expressed as:

฀฀󰇗� ฀฀ ฀฀ ฀฀ ฀฀� (4) � ฀฀󰇗� � = ฀฀�฀฀ ฀฀ ฀฀ ��฀฀󰇗� � ฀�� ฀฀ ฀฀ ฀฀ ฀฀󰇗�� Where The corresponding parameters ฀฀, ฀฀, ฀฀, ฀฀, ฀฀, ฀฀ depend on the type of plasticity theory used i.e. IT or DT and ฀฀ is the Young modulus.

1 ฀฀ = ( ฀฀�� ฀฀�� − ฀฀��� ) ฀฀ 1 ฀฀ = (฀฀�� ฀฀�� − ฀฀�� ฀�� ) ฀฀ 1 ฀฀ = (฀฀��฀฀�� − ฀฀���) ฀฀ 1 ฀฀ = (฀�� ฀฀�� − ฀฀�� ฀฀��) ฀฀ 1 ฀฀ = (฀฀��฀฀�� − ฀฀��฀฀��) ฀฀ 1 ฀฀ = ( ฀฀��฀฀�� − ฀฀���) ฀฀ ฀ ฀฀ ฀฀ ฀฀ �� �� �� ฀฀ = �฀�� ฀฀�� ฀฀��� ฀฀� ฀ �� ฀฀�� ฀฀��

฀฀� ฀฀� ฀� �� � + � � ฀฀� 4฀฀ � ฀฀ � 1 ฀฀� ฀�� = − �1 − (1 − 2฀฀) 2 ฀฀ ฀฀ ฀฀฀ ฀� − 3 �1 − �� � � + � �� ฀฀� 2฀฀ � ฀฀ � 3 ฀฀� 2 ฀฀− ฀฀ ฀฀ ฀�� = �1 − � � � ฀฀� � ฀฀ ฀฀ � 2 ฀฀� ฀฀� ฀฀� ฀�� = 1 − 3 �1 − �� � + � � ฀฀� 4฀฀ � ฀฀ �

(5a)

(5b) (5c) (5d) (5e)

(5f)

฀฀� ฀฀� ฀฀� ฀ � − (1 − 2฀฀) + 9 �1 − � � ฀฀� ฀฀ ฀฀� � ฀฀

(6e)

(6f)

Let ฀฀� = −฀฀, ฀฀� = −฀฀, ฀฀�� = −฀฀ at the point of bifurcation. Assuming that the material is in a state of plane stress i.e. ฀฀� = ฀฀�� = ฀฀�� =0, the effective stress ฀฀� can be expressed as: ฀฀ �� = ฀฀�� − ฀฀�฀฀� + ฀฀�� + 3 ฀฀��� (7) 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) � �฀฀󰇗�฀฀� + ฀฀�󰇗 ฀฀�󰇗 + ฀฀󰇗�� ฀฀�� 󰇗 �฀฀฀฀ 2 The potential energy V for the material subjected to uniform in-plane compressive stresses is given as: � � 1 ฀฀฀฀ ฀฀฀฀ − � �฀฀� ℎ � � + ฀฀� ℎ � � 2 ฀฀฀฀ ฀฀฀ (9) ฀฀฀฀ ฀฀฀฀ + 2฀฀�� ℎ � � � ��฀฀฀฀ ฀฀฀ ฀฀฀ ฀฀ =

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)

(5g)

The aggregate crushing value is calculated by the following equation: Aggregate crushing value % = B/A×100 (11)

According to the deformation theory:

฀�� = 1 − 3 �1 −

861

(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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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]:

∆฀฀ = ฀฀ ฀฀�฀฀�฀฀�

(13)

Where: m=mass of flywheel R=radius of flywheel=0.4m ฀฀=angular speed of rotation of flywheel

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]

฀฀� + ฀฀� ≤ 0. 5

(14)

Where ฀฀� =pitch diameter of pinion ฀฀� =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]. ฀฀฀ 2฀฀� Where: ฀฀ is the bending moment ฀฀ is the thickness of the jaw ฀฀� second moment of inertia

฀฀� =

Fig. 7 Sketch plan view showing mechanism for the crusher

(15)

6. Design 6.1. Operating and principle in detail Fig. 8. Exposed (a)Side view (b) Plan (c) Isometric view

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

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)

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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.

[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 Enginee...