Finite Element Analysis of the Bike Frame

Introduction

Finite element analysis (FEA) allows us to computationally simulate the behaviour of an object when it is subjected to various loading conditions using a digital twin. In the case of the bike frame, it allows us to examine and predict whether or not the frame will fail for various load cases without the need for conducting multiple physical experiments which can both be costly and time consuming. Typically, the results of these simulations will be used to make decisions on how the design can be improved to better handle loads; the new design would then be thrown back into FEA and the process is repeated until the engineer is satisfied with the results. Bear in mind, that FEA is not a replacement for physically performing tensile and fatigue testing, but is a useful tool for developing a design until it reaches a final state where it can then be validated in the real world.

In the context of the bicycle project, Ansys Aim 2020 was used to conduct FEA of the bike frame if a 300 lbs person were to ride it. The FEA results did not show any major areas of concern that required the frame geometry be modified to better handle its load conditions. Ideally, the bike frame design would have been improved based on the simulation results but given the limited time available to us, this was forgone. We have confidence that the FEA results hold true as the geometry of the frame follows the conventional diamond shape, which has become popular for being a strong, stiff, and reliable shape for bike frames. Additionally, the tubes used to build the frame are specifically engineered for bike riding and all the cuts made on the tubes follow the manufacturer's guidelines. In the future, the IDEAs Clinic would like to perform physical life cycle testing on the frame but we are currently not at that stage yet.

Geometry and Material Assignments

The CAD model of the bike frame was created to be as accurate as possible to how it would be once it was built in real life. This means that the 3D model contains every feature the actual frame would have such as varying wall thicknesses in the tubes, correct tube lengths and angles, and an accurate representation of the rear dropouts. Once the geometry was imported into Ansys Aim, each component in the frame was given a steel material assignment. The top tube, head tube, seat stays, and chain stays belong to the Columbus Zona tube family which are all made of 25CrMo4 chromoly steel which has a yield strength of 7.6E8 Pa. The bottom bracket shell and rear dropouts were assumed to be made of the same material as the Columbus Zona tubes since the supplier did not disclose the type of steel these were made of. All the components highlighted in blue in the image below were given a material assignment of 25CrMo4 chromoly steel.

The seat tube and down tube belong to the Columbus Spirit HSS and Columbus Life, respectively. Originally, we were going to purchase these tubes from the Columbus Zona family as well, but due to limited inventory from the supplier we had to find alternatives. Both of these tubes are made of a patented type of chromoly steel that the manufacturer calls Omnicrom steel which has a yield strength of 9.2E8 Pa. All of the components highlighted in blue in the image below were given a material assignment of Omnicrom chromoly steel.

The material properties of the tubes used in the frame can be found here in this catalogue:

The Support Conditions, Coordinate System, and Scale

The supports for each of the simulation scenarios is kept constant; the frame has fixed supports at the rear dropouts and at the bottom face of the head tube as both of these ends are supported by the rear axle and the fork, respectively.

For reference, the coordinate system for the simulation is represented by the image below.

All simulation results shown in this article will be represented on a linear scale and the graphics are automatically scaled to exaggerate the displacement of the frame.

Scenario 1: Riding the Bike Normally

This scenario simulates the behaviour of the bike frame if someone were sitting on the saddle in an upright position like you normally would when riding a bike. It was assumed that in this scenario, about 65% of the rider's weight would be transferred into the seat tube along the y-axis and 35% of the weight would be transferred into the head tube along its axis. For a 300 lbs person, this translates into 195 lbf loaded on the seat tube and 105 lbf loaded on the head tube. 

The results show that the maximum stress that occurs on the frame is 1.11E8 Pa along the joint where the seat tube and down tube meet. This maximum stress is significantly lower than the yield stresses of these two tubes (9.2E8 Pa) so it can be concluded that the frame will not fail at that joint in this scenario.

An imperceptible amount of deflection would occur in this scenario as the the maximum displacement is 1.53E-4 m along the seat stays.

Scenario 2: Front Wheel Hitting a Wall

This scenario simulates the behaviour of the bike frame if the front wheel were to hit a wall violently. It was assumed that in this scenario, about 65% of the rider's weight would be transferred into the seat tube along the y-axis and 35% of the weight would be transferred into the head tube along its axis. For a 300 lbs person, this translates into 195 lbf loaded on the seat tube and 105 lbf loaded on the head tube. A force of 200 lbf is exerted along the inside face of the head tube along the x-axis because the force from the wall would be transferred from the wheel to the fork, its steerer tube, and then eventually the head tube. A more accurate loading condition would take into account the momentum of the bike and the duration of the collision, but for the purposes of a static simulation this should be an adequate representation.

The results show that the maximum stress that occurs on the frame is 1.12E8 Pa along the joint where the seat tube and down tube meet. This maximum stress is significantly lower than the yield stresses of these two tubes (9.2E8 Pa) so it can be concluded that the frame will not fail at that joint in this scenario. The results are similar to the previous scenario but one thing that is different is that there is now a considerable amount of stress that occurs along the bottom of the head tube as a result of the front wheel's collision with a wall.

An imperceptible amount of deflection would occur in this scenario as the the maximum displacement is 1.81E-4 m along the seat stays.

Scenario 3: Riding the Bike While Standing on the Pedals

This scenario simulates the behaviour of the bike frame if the rider was using the bike while standing on its pedals. It was assumed that in this scenario, about 50% of the rider's weight would be transferred into the bottom bracket shell along the y-axis and 50% of the weight would be transferred into the head tube along its axis. This ratio was determined since people tend to lean forward more when standing on the pedals as they ride, transferring more of their weight into the handlebars. For a 300 lbs person, this translates into 150 lbf loaded on the seat tube and 150 lbf loaded on the head tube.

The results show that the maximum stress that occurs on the frame is 6.13E7 Pa along the joint where the seat tube and down tube meet. This maximum stress is significantly lower than the yield stresses of these two tubes (9.2E8 Pa) so it can be concluded that the frame will not fail at that joint in this scenario.

An imperceptible amount of deflection would occur in this scenario as the the maximum displacement is 6.46E-5 m at the bottom bracket shell but the displacement along the seat stays is a close second.

Scenario 4: Abrupt Front Braking

This scenario simulates the behaviour of the bike frame if the rider abruptly slammed their front brakes. It was assumed that in this scenario, about 100% of the rider's weight (300 lbs) would be transferred into the head tube along its axis as the bike would pitch forward. An additional 200 lbf is also assumed to be applied by the rear brakes along the x-axis.

The results show that the maximum stress that occurs on the frame is 5.18E7 Pa along the bottom face of the head tube. This maximum stress is significantly lower than the yield stress of this tube (7.6E8 Pa) so it can be concluded that the frame will not fail along this region.

An imperceptible amount of deflection would occur in this scenario as the maximum displacement is 6.27E-5 m at the top face of the head tube.

Scenario 5: Abrupt Rear Braking

This scenario simulates the behaviour of the bike frame if the rider abruptly slammed their rear brakes. It was assumed that in this scenario, about 100% of the rider's weight (300 lbs) would be transferred into the seat tube along the y-axis as the bike would pitch backwards. An additional 200 lbf is also assumed to be applied by the rear brakes along the x-axis to the rear dropouts.

The results show that the maximum stress that occurs on the frame is 1.72E8 Pa along the joint where the seat tube and down tube meet. This maximum stress is significantly lower than the yield stresses of these two tubes (9.2E8 Pa) so it can be concluded that the frame will not fail at that joint in this scenario.

An imperceptible amount of deflection would occur in this scenario as the the maximum displacement is 2.4E-5 m along the seat stays.

Fatigue Life Analysis of the Frame

The fatigue life analysis results of the frame are identical for the loading scenarios from 1-5. The results all show that the frame will never reach failure after a total of 1 million cycles.

Conclusions

The FEA results clearly show that the bike frame should not fail when subjected to various loading conditions as the maximum stress is consistently less than the yield strength of the tubes. The frame also experiences an extremely small amount of deflection in all of these loading scenarios. The maximum stress that could occur is about 1.72E8 Pa along the down tube and seat tube joint if the rear brakes were abruptly slammed. The maximum displacement that could occur is about 1.81E-4 Pa along the seat stays if the front wheel were to smash into a wall. We can also conclude that the frame will never experience failure due to fatigue which makes sense since steel has a fatigue limit. It is worth noting that these loading conditions were exaggerated to account for the worst cases. All in all, we can conclude that the frame will not fail when we ride it.

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