FEA And Analytical Analysis Of A Bicycle Crank

This task requires you to model a simplified version of a bicycle crank. The crank has been manufactured from 6000 series aluminium alloy with the following properties: E = 70 GPa, v = 0.33. The geometry files for the component have been provided and a schematic of the system is included below 

                                                                         

In addition to the FEA component, you must also:

• produce an analytical solution for the system, calculating appropriate metrics for comparison to your FEA model

• conduct an experiment using the test rig (provided in your computer lab) and record appropriate metrics for comparison to your analytical and FEA models Report

The report must be a 3-4 page technical report and incorporate all of the pertinent information. It must include the following:

• A description of the objectives of the investigation

• A description of the component to be analysed

• A brief summary of the FEA analysis program used

• A relevant analytical solution of the system and analysis of the experimental data (may be included as an appendix, i.e. not counted in word limit)

• A full description of the FEA model, including boundary conditions, loading, meshing and assumptions

• Results of the FEA model with relevant parameters described

• Analysis of the model and its relationship to the analytical solution and experimental test (i.e. verify and validate your model)

• Conclusion and recommendations

Format Guide

1. Font size should be no smaller than size 11 Arial, Calibri (Body) or Times New Roman

2. Page margins should be no smaller than 1.90 cm on the top, bottom, left and right.

3. Front matter such as title and contents pages is not counted in the page limit

4. There is a penalty of 2 marks per page for any extra pages of content included in your assignment (this does not include the hand calculations as an appendix)

About the Component

About the Component

Crank is the component used to connect the pedal and Chain sprocket in the bicycle. The crank converts the reciprocating motion of the legs of the rider into rotational motion of chain sprocket. This sprocket drives the chain which in turns rotates the rear wheel and thus translational motion is produced from the reciprocating motion of the human legs. Cranks are preferably made from aluminium alloy material. Apart from Aluminium some other materials like Titanium, chrome alloy steel and carbon fibre based material is used as per the application.

Geometry

As mentioned in the problem statement the same geometry is created in 3D CAD form using Solidworks (Fig. 5). The geometry is then imported in DesignModeler of Ansys Workbench. Here a 5mm x 5mm patch (Fig. 7) is created at the location where strain Rosette is to be probed. A patch is a face-split feature used to isolate the area under influence. The strain results on this patch are used for validation of simulation results with Strain gauge experiment. The total volume of the component is 38089 mm³ with total weight of 0.10551 kg. (Fig. 6)

Material

As mentioned in the problem statement, 6000 Aluminium Series Grade Material is used. The Material Properties are as below

Density (kg/m3)	2770
Young's Modulus (GPa)	70
Poisson's Ratio	0.33

FEA Approach and Assumptions

• The System of Units used is Metric (mm, kg, N, s, mV, mA)
• We have used ANSYS WORKBENCH v170 to solve the problem.
• The  load P as shown in the figure is applied using Remote Force in Ansys Wokbench
• To validate the simulation with experimental testing we are creating a patch
• (5mm x 5 mm) at the same location where strain rosette is to be probed.      
• FE Model The crank is meshed with Hex Dominant method approach in the Workbench (Fig.2). The total number of elements in the model is 103769 with 432253 nodes.  Initially we had meshed with coarse elements and then slowly we proceeded with mesh refinement.                                                                                                                                                                                                                                                                                                                                                                                           

Loading and Boundary Conditions

Any FE Model cannot be solved for structural analysis without constraining at least its one node in any one of Translational or rotational degree of freedom. The constraints are to be defined as per the practical mounting conditions.

As per the problem statement we have created a Remote Point to apply the eccentric load on the crank. For loading, it has been estimated that a force of 25kgf will be applied at the location shown with load P in the Problem statement (Fig. 1). This force is applied as 250N (~25 kg*9.81 m/s²) in the Ansys in vertically downward direction from the Remote Point created and scoped to circular hole in the crank (highlighted in red in Fig. 3). The inner surface (highlighted in blue in Fig. 3) of the square hole of the crank is fixed. It means that all the nodes on the surface of that surface will have no (zero) translational and rotational displacements in all the directions. Both the conditions are shown in Fig. 3 below.

Geometry

                                                                                

Results

For given loading and boundary conditions with 6000 series Aluminium grade material, the maximum deformation in the crank is 1.0166 mm at the load end (circular hole) of the crank. Whereas the maximum stress induced is 96.186 MPa which is the fixed location. The location where crank has step in the geometry at the fixed end, stresses induced are more.  Using Ansys Parametrization feature, I did a simple Design of Experiments (DoEs) by changing the load values and observing the change in results. The results of same are attached in Appendix : Table 1.

Summary

After successful completion of execution of simulation of the crank in the model I was able to learn many things. The most important thing is Finite Element Analysis is mathematical approximation technique. The results are dependent on mainly two things : (1) The quality, type and Size of Mesh (Element Model) and (2) The inputs we define: i) Material Properties ii) Loading and Boundary Condition and iii) The solver used. After performing this exercise I am confident to simulate different components by application perspective.

Conclusion

From this exercise we can conclude things mentioned as below:

• As the load increases the stresses induced increases.
• The stress induced near the fixed end maximum whereas the deformation is more at the other end.
• The behaviour of crank is analogous to the behaviour of the cantilever beam loaded at free end.
• To reduce the stresses the steps at the ends should smooth curve.
• If possible undercut can also be made to reduce the stresses. Similar provisions are made in the rotating shafts.
• As the force acting on the crank is generated from human energy there is rarely any fluctuation in load and also there are very less changes of any occasional or impact load.
• The crank should not only survive the loads but also to the repeated loads. We can estimate the life of the crank using Fatigue Analysis.
• If the Factor of safety in the component is above 3 then we can go Topology Optimization to reduce the material, weight and cost of the component.