INTRODUCTION Cycling is very common and famous sport and way of travelling at the same time. Human powered vehicle can be ideal means of transport, sport and fun for friends, who want to travel together and spend their free time actively. Among the components of bicycle, the crank arm is the most important component for a bicycle to move forward.
Figure 1 Bicycle crank arm
Bike crank is the component of a bicycle that converts the reciprocating motion of the rider's legs into rotational motion. The motion is use to drive the chain and turn the wheel of the bicycle when moving. This crank is the most important part of a bicycle since it is where the motion is produced to move the bicycle. The importance of this crank arm is so great, that the design and the analysis of the crank arm need to be done thoroughly in order for the bicycle to be safe for riding. For the purpose of this project, a simple design of the crank arm and pedal is used to be analysed. The finite element analysis will be done solely by using the ANSYS software, where using this software, the steady state analysis will be done upon the design and the largest displacement as well as the weakest point on the design will be determined.
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OBJECTIVE Finite element method is a numerical procedure that can be applied to obtain solutions to a variety of problems in engineering. The objectives of FE Analysis are as follow: 1. To predict the behaviour of the material/system. 2. To apply the geometric modelling. 3. To build a complicated object with simple object. However, the purposes of the finite element analysis upon the design in this project are: 1. To apply the basic steps of finite element analysis by using the ANSYS software to model the object. 2. To apply mesh, boundary conditions and loads and to solve them. 3. To determine the largest displacement and the weakest point on the model through the functions available in the ANSYS software. DETAILS OF OBJECT In this project, some assumptions to the material used as well as the important dimension of the object are made to model the object and to obtain results. The physical attributes of the bicycle crank arm modelled in this project are as follow: Physical Attribute
Value Material Used: Steel
Young's Modulus of Elasticity
2 MPa
Poisson's Ratio
0.32
Pressure applied
10 kN Important Dimension
Crank arm length
230 mm
Crank arm height
30 mm
Crank arm thickness
10 mm
Crank arm hole diameter
20 mm
Pedal length
90 mm
Pedal diameter
20 mm
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The crank arm of the bicycle is modelled based on the design and dimensions as stated above. The model is basically done using the application of extrusion of areas and Boolean's methods of addition and subtraction.
Figure 2 Solid model of crank arm of a bicycle
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Boundary Condition After modelling the object and saving the project, the element type and the material properties of the object are determined. Then the boundary condition of the object are set. For this object, the boundary condition of displacement at the circular hole are set to zero in all Degree of Freedom (DOF). This is because, we did not want the hole to move from its position in real life since the hole is where the shaft is positioned. Next, point load is exerted on to the crank arm's pedal. The load of 10 kN is positioned on the node at the end of the pedal arm. This is where most bicyclist will exert most force when riding the bicycle. Meshing Next, the model is meshed. For the purpose of this project, the model is meshed for two times, each with different element size: 1. Element size 1.0 2. Element size 0.8 (Smaller by 20% from the first attempt)
From each attempt, the deformed and un-deformed shape, as well as the Von Mises stress solution are obtained. These solutions are then compared and the maximum deflection as well as the weakest point on the model will be known.
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Element size of 1.0
Figure 3 Mesh figure of element size 1
Figure 4 Deformed and Undeformed shape when element size is 1
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Figure 5 Stress Von Mises Diagram when mesh element size is 1
From Figure 4 and Figure 5, the maximum value of the deflection that occur to the model is obtained. The maximum deflection resulted to 5.398 mm while the maximum Von Mises stress value is 5103 MPa where the weakest point on the object lies.
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Element size of 0.8
Figure 6 Meshed object of element size 0.8
Figure 7 Deformed and Undeformed shape when mech element size is 0.8
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Figure 8 Stress Von Mises Diagram when mesh element size is 0.8
From Figure 7 and Figure 8, the maximum value of the deflection that occur to the model is obtained. The maximum deflection resulted to 5.823 mm while the maximum Von Mises stress value is 5552 MPa where the weakest point on the object lies. Result Comparison The values obtain from both model are compared with each other. The results compare well with the finer mesh contours being smoother as expected. The largest deflection on the object as well as the weakest point on the object are as follow: Mesh Element Size
1.0 (Coarse)
0.8 (Fine)
DMX
5.398 mm
5.823 mm
SMX
5103 MPa
5552 MPa
The maximum displacement value changes by less than 8% and the maximum von Mises stress value by less than 9%. This indicates that the meshes used provide adequate resolution since the changes are small. Hence, we can tell that even if we reduces the size of mesh, there will not be huge differences in the value since it has already achieve the mesh independence condition. Computer Aided Engineering Design | Page 9 of 10
CONCLUSION Bicycle crank has been selected as the object for this mini project. In order to produce an appropriate design for the object, some assumptions are made for the object, in term of material type, boundary conditions and load values. From the assumption made, the largest displacement and the weakest point gathered from the Von Mises stress plot of the object were obtained. The meshing process are done for a few times with different element size. This procedure is done in order to obtain a more accurate result from the model. Finer mesh enables the ANSYS software to give out more accurate data. However, when the reduced element size mesh does not bring any huge difference in the values obtained anymore, we can conclude that the value obtained is adequate enough for the model and that having more finer mesh will not bring any better result since the mesh independence has already been determined. Hence, through this project, the behaviour of the material for the bike crank has been predicted. From this project, we find out that the maximum deflection of the object will occur at the point where the load is applied and will have a value ranging between 5.0 6.0 mm. While the weakest point on the object can be determined by knowing the point where the maximum Von Mises stress occur, which on this object, it will range between 5000 - 6000 MPa. Thus, the objectives of the Finite Element Analysis are achieved in this mini project.
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