FEM ANALYSIS

A structural FEM analysis was carried out on the final design of the swingarm. The jump over kerb situation was studied, because in this condition the structure reach the greatest stresses and deformations compared with the other cases in which the forces acting on the swingarm are significantly lower.

Indeed, in the situation of jump over kerb, the force transmitted to the motorbike is approximately equal to five times the total motorbike weight, i.e. the bike's plus the pilot's weights. This force is then multiplied by a factor of safety of 1.5. So the total force acting on the rear wheel in this condition is 6953N (for the computation see the force analysis page).

The swingarm model was examined in Abaqus FEA (a Dassault Simulia software) and in the CATIA V5 "Generative Structural Analysis" module for static analyses. The results coming from the two softwares were very similar each other, but the second one was used because of its reliability and quickness in preparing the assembly model for the simulation. Abaqus was mostly used to check the results.

The model was constrained for structural analysis using a hinge (three degree of freedom locked) in the pivot  and sliders (two d.o.f. locked) in the rearward hub housings, in the two aluminum plates. The two equivalent forces applied to the shock-absorber attachment and to the pro-link attachment were computed starting from data coming from the other pro-link teams and obtained by using an equilibrium of moments around the pivot hinge. Then each force was splitted in its Z and Y (vertical and longitudinal) components and "applied" as a distributed force to the two holes of each attachment  point. Then the mesh was set and the analysis executed.

This model best represents the real condition of the motorbike.

The following pictures are the results from the CATIA simulation:

Von Mises stresses

Deformation

The stress values are well under the yield point of the material. This is typical of most motorbikes, because the swingarm must have a great stiffness and not only to be strong enough to withstand the maximum load.

Looking at the results of the FEM analyses it is evident that there are not points in which numerical divergency occurs (sometimes it's possible to have isolated points with stresses very different form the adjacent ones).

Analysis of the misalignment of the connection with pro-link:

By measuring the deformation of two symmetric points with respect to the mean one on the pro link attachment, it can be noted that the difference in displacement is of the order of 10^-2 mm.

These results have to be interpreted taking into account the fact that such small displacements can also be affected by numerical errors. The force is transmitted by the pro-link through a pin, so its misalignment is really negligible, it  depends on the material of the pin and since it’s very short its deformation is close to zero. This fact guarantee a correct operation of the axle box through which the pro-link is attached to the swing arm. Furthermore a plastic part is used in the contact part between the two components to avoid the wear of the metallic part and it’s easily interchangeable after its life time.

FEM analysis with Abaqus

In order to have a feedback about the correctness of our previous analysis, the same FEA was repeated using another software: Abaqus.

Considering that, from Catia Analysis, the two aluminum tip plates have very low deformations, it is possible to state that, with good approximation, they behave like rigid bodies. Therefore, to simplify the computational load of further analysis, such components were removed and substituted with pins applied in the six holes. This allows to have a much easier part and thus to use a smaller mesh (having higher precision of the results). However, there are no significant losses in terms of reliability of the results.

  The results are very positive: this analysis proves that the Catia analysis was correct. By a qualitative point of view, the most stressed points are close to the attachment of the prolink and also the distribution of Von Mises stress is very similar to the one found with Catia. Also displacements have very similar distribution, in the two analyses. By a quantitative point of view, Abaqus returns maximum stress and deformation values which are similar and slightly lower than the ones of Catia. This small difference can be explained with the absence of the two tip plates.

Comparison between the swingarm with or without stiffening elements:

A useful coefficient used in swingarm design is the ratio between the difference in stiffness and mass of two models:

ε = Δstiffness / Δmass       (where stiffness = force applied / maximum displacement)

A higher value of ε is related to a more efficient effect of the stiffening elements

Without stiffening elements:

Stiffness = 16365 N/mm

With stiffening elements (see the first pictures):

Stiffness = 38941 N/mm

Δmass=0.9Kg

ε = 25 N*Kg/mm

The increase in stiffness is substantial, so the lateral stiffening elements can highly decrease the maximum deformation (from 0.86 to 0.3mm) with a rather low increase in mass.