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Finite Element Analysis On A Bicycle Crank

ME-371 Class Project

11/24/2008

Mazen Diab

Syed S Hasan

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Table of Contents ABSTRACT ...................................................................................................................................................... 3

INTRODUCTION ............................................................................................................................................. 3

PROCEDURE .................................................................................................................................................. 3

SUMMARY OF PROCEDURE .......................................................................................................................... 4

RESULTS & DISCUSSION ................................................................................................................................ 4

CONCLUSION ............................................................................................................................................... 12

REFERENCES ................................................................................................................................................ 12

LIST OF FIGURES ...................................................................................................................................... 12

LIST OF TABLES .................................................................................................................................... 12

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ABSTRACT The maximum stress and the maximum displacement have been determined to be approximately 120 MPa and 0.02mm respectively. Through various studies it has noticed that the stress and displacement increases as the quality of the mesh changes with the type as well. Even though the change is small but it does occur. Moreover, the changing in the method from normal to the p-adaptive as well causes the stress and displacement to be changed. Since the yield strength for the bicycle crank has found to be approximately 350 MPa whereas, the stress has found to be approximately about 120 MPa the bicycle crank. Thus it can easily be said that the bicycle crank will not deform and break within the determined range of stress.

INTRODUCTION

Load/Type Restraint Type Material Study Type 500N/Normal Fixed Steel 1020 Static solid mesh

Table 1 (shows condition)

PROCEDURE SOLID MODELING

1. The dimensions were given to create the bicycle crank. 2. Using the specific dimensions the bicycle crank was modeled in a solid work. 3. Once the model was created it was required to run in COSMOS Works to analyze the maximum

stresses.

COSMOS WORKS

1. The analysis manager was selected from the manager tree. 2. The study was created and the material was assigned as steel 1020. 3. The restraint was applied at the hole. 4. The normal load of 500N was applied at the right side 5. The several studies were generated and stress change had been determined by creating coarse,

medium and fine mesh of the draft and high quality. 6. For better understanding the mesh control has applied and then run the mesh to create the

stress plot. 7. First few studies the normal method have been used and then studies were done by using p-

adaptive method. 8. Under the p-adaptive method the draft quality mesh was not compatible thus high quality

options were used.

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SUMMARY OF PROCEDURE Study # Mesh Type Mesh Quality Method Jacobian Type Mesh Control 1 Coarse Draft Normal At 4-points None 2 Medium Draft Normal At 4-points None 3 Fine Draft Normal At 4-points None 4 Coarse High Normal At 4-points None 5 Medium High Normal At 4-points None 6 Fine High Normal At 4-points None 7 Coarse Draft Normal At 4-points At max. stress 8 Medium Draft Normal At 4-points At max. stress 9 Fine Draft Normal At 4-points At max. stress 10 Coarse High Normal At 4-points At max. stress 11 Medium High Normal At 4-points At max. stress 12 Fine High Normal At 4-points At max. stress 13 Coarse High p-adaptive At nodes None 14 Medium High p-adaptive At nodes None 15 Fine High p-adaptive At nodes None 16 Coarse High p-adaptive At nodes At max. stress 17 Medium High p-adaptive At nodes At max. stress 18 Fine High p-adaptive At nodes At max. stress

Table 2 (summary of detailed procedure)

RESULTS & DISCUSSION

Figure 1 coarse quality mesh & draft type

Figure 2 the maximum stress coarse-draft

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Figure 3 Medium quality mesh draft type

Figure 4 Maximum stress medium draft

Figure 5 Fine quality mesh draft type

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Figure 6 Maximum stress fine draft

Figure 7 Coarse mesh quality high type

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Figure 8 Maximum stress coarse high

Figure 9 Medium quality mesh high type

Figure 10 Maximum stress medium high

Figure 11 Fine mesh quality high type

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Figure 12 Maximum stress fine high

The pictures above show the various of the mesh quality and the type of the mesh has applied during the various studies. Also the other pictures indicate the maximum stress that has occurred in the bicycle crank. However, the tables below show the other required information.

Max. Stress (MPa)

Max. Axia Displacement (mm)

Total # of Elements

Total # of Nodes

Total # of DOF

Global Size (in)

Global Size (in)

Running Time (sec)

41.112 0.01751 3736 1016 2931 0.01676 0.3351 5 51.053 0.01826 5978 1575 4635 0.00922 0.18431 4 77.486 0.02000 57080 12007 35580 0.00419 0.0838 15 101.101 0.02086 3736 6443 18915 0.01676 0.3351 4 101.924 0.02119 8578 14133 41787 0.00838 0.1676 6 118.900 0.02129 57080 85907 256083 0.00419 0.0838 30

Table 3 Results of study 1 through 6 without mesh control

Max. Stress (MPa)

Max. Axia Displacement (mm)

Total # of Elements

Total # of Nodes

Total # of DOF

Global Size (in)

Global Size (in)

Running Time (sec)

48.666 0.01785 4028 1087 3144 0.01676 0.3351 4 64.680 0.01868 14015 3363 9999 0.00922 0.18431 4 77.486 0.02000 57080 12007 35580 0.00419 0.0838 15 112.524 0.02085 4030 6919 20343 0.01676 0.3351 4 100.961 0.02121 8948 14701 43491 0.00838 0.1676 7 118.900 0.02129 57080 85907 256083 0.00419 0.0838 32

Table 4 Results of study 7 through 12 with mesh control

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Max. Stress (MPa)

Max. Axia Displacement (mm)

Total # of Elements

Total # of Nodes

Total # of DOF

Global Size (in)

Global Size (in)

Running Time (sec)

113.916 0.02143 1208 2342 6792 0.01676 0.3351 10 113.677 0.02139 7944 13121 38859 0.00838 0.1676 20 118.554 0.02133 54816 82567 246243 0.00419 0.0838 107

Table 5 Results of study 13 through 15 p-adaptive methods without mesh control

Max. Stress (MPa)

Max. Axia Displacement (mm)

Total # of Elements

Total # of Nodes

Total # of DOF

Global Size (in)

Global Size (in)

Running Time (sec)

114.060 0.02144 1432 2744 7998 0.01676 0.3351 11 111.213 0.02139 7784 12919 38253 0.00838 0.1676 18 118.554 0.02133 54816 82567 246243 0.00419 0.0838 106

Table 6 Result of study 16 through 18 p-adaptive methods with mesh control

The above table shows that the maximum stress and the maximum displacement in x-direction increases when the mesh type and the quality changes. The table indicates that the maximum stress and the displacement have found to be greater when the mesh type is fine and the mesh quality is high. On the other hand, the maximum stress and the maximum displacement have found to be the lower when the mesh type is coarse and the quality of the mesh is draft. Similarly using p-adaptive method obtains the same results. The higher and finer the mesh the greater the maximum stress and the maximum displacement in x-direction.

During some studies the meshing has teken some time it tells that the meshing control has been applied to determine the maximum stress. In some studies when the meshing control has changed to 0.01 the study was abort automatically. From this such analogy can be made that the mesh control can be applied but cannot be taken very small which allow the study to abort or finish without any affect.

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Figure 13 Graph showing maximum stress for various studies

The graph shows the maximum stress that has occurred in each study is done; also it indicates that there is a pattern of increasing the maximum stress as the quality and the type of mesh changes. It is noticed during the various study that in the bicycle crank the stress will be maximum when the mesh type is fine and the mesh quality is high. Thus the maximum stress through the various studies have found to be approximately about 120 MPa

0

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120

140

1 2 3 4 5 6 7 8 9 10 11 12

Max

. Str

ess

(Mpa

)

Study #

Maximum Stress from various study 1 Through 12

Max Stress(Mpa)

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Figure 14 Graph showing maximum displacement for various studies

The graph shows the maximum displacement that has occurred in each study is done; also it indicates that there is a pattern of increasing the maximum displacement as the quality and the type of mesh changes. It is noticed during the various study that in the bicycle crank the displacement will be maximum when the mesh type is fine and the mesh quality is high. Thus the maximum displacements through the various studies have found to be approximately about 0.02 mm.

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Max

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t (m

m)

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Max. Displacement for various study 1 through 12

Max Displacement (mm)

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CONCLUSION In conclusion through the various studies that have done on the bicycle crank the maximum stress and maximum displacement have been recorded. The stress and the displacement increases when the normal load applies on the shaft of the bicycle crank when the quality is high and the mesh type is fine. Similarly when the loading method is changed from normal to the p-adaptive method the stress and displacement further gets higher than the normal when the quality and the type of mesh is high and fine respectively. Through the studies it has been the adaptive method does not change the local size or element the only effect occurs during the adaptive method is the mesh is finer than the normal method and the stress is much greater than normal as well.

The yield strength for the following bicycle crank has found to be approximately about 350 MPa thus it can easily be said that the maximum stress that is found to be approximately 120 MPa lies within the range. Thus the bicycle crank will not deform and break when 500N load is applied normal to the right side of it.

REFERENCES 1. Mazen Diab, Finite Element project document & class notes. 2. P. M. Kurowski , Static Analysis of a plate (solid work manual) 3. P. M. Kurowski , Static Analysis of an L-Bracket (solid work manual) 4. P. M. Kurowski , p-Element (solid work manual)

LIST OF FIGURES Figure 1 coarse quality mesh & draft type .................................................................................................... 4 Figure 2 the maximum stress coarse-draft ................................................................................................... 4 Figure 3 Medium quality mesh draft type .................................................................................................... 5 Figure 4 Maximum stress medium draft ....................................................................................................... 5 Figure 5 Fine quality mesh draft type ........................................................................................................... 5 Figure 6 Maximum stress fine draft .............................................................................................................. 6 Figure 7 Coarse mesh quality high type ........................................................................................................ 6 Figure 8 Maximum stress coarse high .......................................................................................................... 7 Figure 9 Medium quality mesh high type ..................................................................................................... 7 Figure 10 Maximum stress medium high ...................................................................................................... 7 Figure 11 Fine mesh quality high type .......................................................................................................... 7 Figure 12 Maximum stress fine high ............................................................................................................. 8 Figure 13 Graph showing maximum stress for various studies .................................................................. 10 Figure 14 Graph showing maximum displacement for various studies ...................................................... 11

LIST OF TABLES Table 1 (shows condition) ............................................................................................................................. 3 Table 2 (summary of detailed procedure) .................................................................................................... 4 Table 3 Results of study 1 through 6 without mesh control ......................................................................... 8

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Table 4 Results of study 7 through 12 with mesh control ............................................................................ 8 Table 5 Results of study 13 through 15 p-adaptive methods without mesh control ................................... 9 Table 6 Result of study 16 through 18 p-adaptive methods with mesh control .......................................... 9