Fatigue Analysis of Bike Crank Arm

Abstract: -

This project aims to perform a fatigue analysis on a bicycle crank arm using SolidWorks and find out the number of cycles it will take before the part to reach failure. The Stress Life (SN) method was used since it is based upon standard material test to failure. Several parameters were changed, these parameters are the geometry of the crank arm, the material selection and finally the loads applied to the crank arm.

Introduction: -

Fatigue: Fatigue is a phenomenon that is observed that repeated loading and unloading weakens objects over time even when the induced stresses are considerably less than the allowable stress limits.  Each cycle of stress fluctuation weakens the object to some extent. After several cycles, the object becomes so weak that it fails. Fatigue is the prime cause of the failure of many objects, especially those made of metals. Examples of failure due to fatigue include rotating machinery, bolts, aeroplane wings, consumer products, offshore platforms, ships, vehicle axles, bridges, and bones.

Stress: is the amount of internal force per unit area, the formula of stress can be shown below:

Stress can be tensile (positive) or compressive (negative). Von mises stress states that a ductile material starts to yield at a location when the von Mises stress becomes equal to the stress limit. In most cases, the yield strength is used as the stress limit. However, the software allows you to use the ultimate tensile or set your stress limit.

Stress- Life Cycle (S-N) Curve: Fatigue strength is determined by applying different levels of cyclic stress to individual test specimens and measuring the number of cycles to failure. The graphical representation of fatigue data points is the cyclic stress amplitude or alternating stress (S - vertical axis) versus the number of cycles to failure (N - horizontal axis). Fatigue strength is defined as the stress at which fatigue failure occurs at a given number of cycles. A typical S-N curve is shown below.

Figure 1: Typical S-N curve

Fatigue life: The number of cycles required to cause failure due to fatigue.

Bicycle crank arm failure can be prevented early on by using dye penetrant testing on the component during the relatively short crack propagation phase

Common places of bike crank failure are shown below, The two most common failures are the pedal eye and the junction of the trailing spider leg and the right crank. The trailing spider leg adjacent to the crank generally has a thin web that connects it to the more rigid shaft of the crank. Stress is concentrated at this web, while the three preceding legs are more flexible. Spider-leg cracks are relatively benign because they are easily seen and rarely progress to failure

Figure 2: crank arm failures

 

Another case of fatigue failure in a bicycle crank spider arm. This was a high-quality component that had very high load cycles but was in excellent apparent condition until the final fracture that unseated the rider in heavy city traffic. The crack progressed slowly through the crank arm (dark area) until the remaining fragment was incapable of supporting the bending moment generated by the force on the pedal and the crank arm fractured rapidly. Removing a pedal ridden for a longer time reveals erosion in the crank face, with tiny cracks radiating from its circumference. In time, some of these cracks propagate into the crank and cause the end of the pedal eye to break off, releasing the pedal, usually at the worst possible moment, that of high stress of a rider pedalling in the standing position

   

Figure 3: another form of failure in the crank arm          

 

 Figure 4: A closer view of the fracture of the crank arm

Procedure: -

For designing the model

1. Sketch the model in Solidworks
2. Extrude it

Figure 5 shows the dimensions of the crank arm.

Figure 5: Dimensions of the crank arm

 

Figure 6 shows the 3D model of the arm

Figure 6: Three-dimensional model of the crank arm

 

For this project, 3 parameters were changed: 

1. The amount of force applied
2. The geometry of the arm
3. The material type

The first simulation is changing the amount of force applied, for the first test a 1000N was applied and a 1500N was applied for the second test.

To start the simulation, a material has to be applied to the crank. Aluminium 6061 – T6 was the chosen material for both models

Figure 7 shows the properties of the material

 

Figure 7: Aluminium 6061 – T6 properties

 

The next step of the simulation is to apply a fixed relation to the holes of the crank arm and apply a force of (1000N for the first test and 1500N for the second test) on the hole of the arm. Figure 8 shows the fixtures and loads for both tests.

Figure 8: Boundary conditions of the bicycle crank arm

 

After setting the boundary conditions we mesh the model, figure 9 shows the mesh parameters used for both studies.

Figure 9: mesh parameters

 

And Figure 10 shows the meshed model of the crank arm for both designs.

 

Figure 10: The meshed model of the Crank arm model.

 

Von Mises Stress Results: -

The maximum Von Mises stresses obtained is 185.9 N/mm^2 for the model in the first test as shown in Figure 11 and 635.760 N/mm^2 for the model in the second test in figure 12

Figure 11: Stress values of the first test

 

Figure 12: Maximum Von Mises stress plot for the 2nd test

 

Fatigue Analysis: -

The finite element model and the boundary conditions remain the same as that of static analysis. The S-N curve for Aluminium 6061-T6 is shown in Figure 13 and the typical curve data for the material is also shown in Figure 14.

Figure 13: S-N curve for Aluminium 6061-T6

 

Figure 14: S-N curve data for Aluminium 6061-T6 in SolidWorks material library

 

The fatigue life of the component is determined by referencing the graph when required alternating stress and the number of required cycles are provided as the input to the Solid works fatigue analysis solver.

The constant amplitude fatigue event is fully defined by alternating stress, mean stress (or stress ratio), and the number of loading cycles. For this project, fully reversed fatigue event was used, it is defined as the alternating stress at each node equal to the selected stress value (stress intensity, von Mises, or P1) from the reference static study times the scale factor. The maximum and minimum values of stress components are equal in magnitude and opposite in direction.

Figure 15: graph of a fully reversed graph

 

For this project, the value R (reference test conditions) are -1 and 0. R=-1 is called the fully reversed condition and R=0, is called pulsating tension.

In this analysis, Minimum stress      

= -1000N

And the Maximum stress

= 1000N

Hence the stress ratio, R=  = -1

 

Fatigue Analysis Results: -

Figure 16 shows the total life plot of component and failure affected area for the first test and figure 17 shows the total life plot of component and failure affected area in the second test.

Figure 16: Plot of the total life of component and failure affected area for the first model.

 

 

Figure 17: Plot of the total life of component and failure affected area for the second model.

 

 

Total life is the total number of cycles that leads to failure at a location in a model, the location is the convergence point between Stress which is a horizontal line and SN curve. Life = N – ΔN, Figure 18 shows the damage percentage for the first test.

Figure 18: Plot of damage percentage of component for the first test

 

Figure 19: Plot of damage percentage of component for the second model

 

The damage percentage of a component is the representation of life in percentage, which is the number of cycles consumed. Damage = N/(N - ΔN). One per cent value signifies that the applied fatigue events observe 100 per cent of life of the model at that point.

 

Observation:-

From 16 we see that the lifecycle fails at around about 3000 cycles for the first test while in the second test it only lasts for 740 cycles, this shows that the crank arm is not strong enough to hold a force of 1500N for a long period of time, as we can see the major locations of the failure is in the neck area which is extremely critical to fatigue loads and cracks at that region. Increasing the neck curve radius will decrease the damage percentage of the neck arm.

 

For the second part of the project, the aim is to see how can a metal effect the fatigue of the arm. Like the first part, 2 tests will be simulated, one with the same material (Aluminium 6061 – T6) and one with the new material (Cast Alloy steel). Figure 20 shows the properties of Cast Alloy Steel.

 

Figure 20: Cast Alloy Steel properties

 

Just like in part one of the project, the loads and fixtures will be the same for both tests. A force of 1000N will be applied on the hole of the arm just like in Figure 8 for both tests. Mesh Parameters will also be the same as in Figure 9 for both tests.

Von Mises Stress Results: -

The maximum Von Mises stresses obtained is 185.9 N/mm^2 for the model in the first test as shown in Figure 11 and 192 N/mm^2 for the model in the second test in figure 21

 Figure 21: Maximum Von Mises stress plot for the 2nd test

 

Fatigue Analysis: -

The finite element model and the boundary conditions remain the same as that of static analysis. The S-N curve for Cast Alloy Steel is shown in Figure 22 and the typical curve data for the material is also shown in Figure 23.

Figure 22: S-N curve for Cast Alloy Steel

 

Figure 23: S-N curve data for Cast Alloy Steel in the SolidWorks material library

 

Similar to part one, the stress ratio, R=  -1. fully reversed fatigue event was used too.

 

Fatigue Analysis Results: -

Figure 16 shows the total life plot of component and failure affected area for the first test and figure 24 shows the total life plot of component and failure affected area in the second test.

Figure 24: Plot of the total life of component and failure affected area for the second model.

 

Figure 18 shows the damage percentage for the first test and Figure 25 shows the damage percentage for the second test

Figure 25: the damage percentage for the second test.

 

Observation:-

As Figure 16 shows, lifecycle fails at around about 3000 cycles for the first test, while for the second test lasted about 352,000 cycles which is a much larger value than the first test. This shows that alloy steel is a much more durable material than the aluminium alloy. In figure 25, the damage percentages are extremely low compared to the values of the first test shown in figure 18.

 

For the last part of the project, the changed parameter is the dimensions of the crank arm, Figure 5 shows the dimensions of the crank arm for the first test and Figure 26 shows the new dimensions of the crank arm for the second test.

Figure 26: new dimensions of the crank arm for the second test

 

Figure 27 shows the 3D model of the arm

Figure 27: Three-dimensional model of the crank arm for the second test

 

 The conditions of part 3 are similar to part 1 and 2, the conditions are as follows:

1. the loads and fixtures will be the same for both tests.
2. A force of 1000N will be applied on the hole of the arm just like in Figure 8 for both tests.
3. Mesh Parameters will also be the same as in Figure 9 for both tests.
4. Aluminium 6061-T6 was used for both tests.

 

Von Mises Stress Results: -

The maximum Von Mises stresses obtained is 185.9 N/mm^2 for the model in the first test as shown in Figure 11 and 195.8 N/mm^2 for the model in the second test in figure 28

 

Figure 28: Maximum Von Mises stress plot for the 2nd test

 

Fatigue Analysis: -

The finite element model and the boundary conditions remain the same as that of static analysis. The S-N curve for Aluminium 6061-T6 is shown in Figure 13 and the typical curve data for the material is also shown in Figure 14. Similar to part one and two, the stress ratio, R=  -1. fully reversed fatigue event was used too.

 

Fatigue Analysis Results: -

Figure 16 shows the total life plot of component and failure affected area for the first test and figure 29 shows the total life plot of component and failure affected area in the second test.

 

Figure 29: Plot of the total life of component and failure affected area for the second model

 

Figure 18 shows the damage percentage for the first test and Figure 30 shows the damage percentage for the second test.

Figure 30: Plot of damage percentage of component for the second model

Observation:-

 In Figure 29, the life cycle is 2472 cycles. This is lower than the life cycle shown for part 1(test one) and part 2 ( both tests). This shows that lengthening the crank arm had a negative effect on the crank arm durability. 

Table Summary:-

The table below shows all the values gathered for the three parts of the project.

Table 1: Summary of data gathered in the project.

Part number	Parameter changed	Mass properties (grams)	Maximum Von Mises Stress (Mpa)	Minimum Life Cycle	Maximum Damage %
1	Force Applied	348.10	185.9 (Test 1)	3006.539 (Test 1)	33.261 (Test 1)
		348.10	635.760(Test 2)	741.975 (Test 2)	134.775 (Test 2)
2	Material type	348.10	185.9 (Test 1)	3006.539 (Test 1)	33.261 (Test 1)
		1000	192 (Test 2)	352,465.781   (Test 2)	0.284 (test 2)
3	The geometry of the Crank Arm	348.10	185.9 (Test 1)	3006.539 (Test 1)	33.261 (Test 1)
		420.35	195.8 N (Test 2)	2472.246 (Test 2)	40.449 (Test 2)

 

Final Conclusion: 

In Parts 1,2 and 3, the crank arm exhibited several changes to its durability and life cycle when it comes to changing the parameters. In part 1, the results show that the material was not strong enough to hold a force of 1500 N for a very long time, this is due to a lot of things, the material of the product, the structural rigidity of the crank arm and the size of the crank arm. In part 2, It is shown that Alloy steel is a much better material than aluminium alloy when it comes to durability and probability of damage occurring to the crank arm. However, Economical and structural aspects must be taken into account and despite alloy steel being a better material, it is more expensive than aluminium alloy and a lot heavier than it.  In part 3, the results found that lengthening the crank arm resulted in a low life cycle and a relatively high probability of damage. 

References: -

1. https://help.solidworks.com/2019/english/SolidWorks/cworks/c_SN_Curve.htm
2. https://help.solidworks.com/2014/English/SolidWorks/cworks/c_Single_Fatigue_Event.htm
3. https://setherickson.wordpress.com/2014/07/30/bicycle-crankset-design-analysis-2/
4. https://www.researchgate.net/publication/328658341_Fatigue_failure_analysis_of_bike_crank_arm_using_solidworks_simulation
5. https://help.solidworks.com/2019/english/SolidWorks/cworks/c_Fatigue_Analysis.htm
6. http://technology.open.ac.uk/materials/mem/mem_ccf4.htm
7. https://web.archive.org/web/20070101155859/http://pardo.net/pardo/bike/pic/fail/FAIL-001.html
8. https://www.sheldonbrown.com/brandt/breaking-cranks.html#:~:text=The%20two%20most%20common%20failures,leg%20and%20the%20right%20crank.&text=In%20contrast%2C%20the%20most%20common,apparent%20to%20a%20critical%20observer.
9. https://www.metalsupermarkets.com/10-differences-aluminum-stainless-steel/