*Giacomo Sarti – giacomo.sarti88@gmail.com*

* Degree in Aerospace Engineering – Prof. Roberto Lot*

## 1. Objective

The aim of this work is to design an innovative swingarm starting from the study of two typical swingarms that are commons in competition motorcycles.

The first swingarm that will be shown is the dual-sided swingarm made in carbon fiber composite. Then, the second swingarm type will be the single-sided swingarm made in aluminium. At the end of the work we see an original swingarm that combines the characteristics of the others two: a single-sided swingarm made in carbon fiber composite.

In this study, for vibration analysis we used the FEM software Patran-Nastran, to draw the model we used Solidworks and for calculation analysis we used Matlab.

## 2. Carbon fiber swingarm

This particular type of swingarm is very used in competition motorcycles. For example, we can see it in Ducati Desmosedici GP07 (MotoGP World Championship, 2007) and in Cagiva C595 (500 cc Word Championship, 1994). Those two Italian bikes will became the dream of every motorcycles fan.

In the picture below we can see the CAD-model of the component. Three materials made this type of swingarm:

- carbon fiber for the “body” of the swingarm
- aluminium for the front part of the swingarm
- titanium for the end part where the wheel will be locked.

Then, this classical-type of swingarm has two holes: the biggest has the function to accommodate the shock absorber, and the small hole allows the passage of the chain.

The figures below show the geometry imported in Patran and the mesh of the component.

The model designed is made by 2D plates for the carbon fiber body and the alumium part, and the thickness of those plates is 3.36 mm.

The ply sequence of the carbon fiber composite is:

*[0 / 90 / +45 / -45 / +45 / -45 / 0 / 90 / 0 / 90 / +45 / -45 / 0 / 90] _{s}*

Before starting the analysis, we add at the swingarm the wheel and the wheel axle simulated respectively like a concentrated mass and like a beam.

Considering all those components the total mass is approximately 14.50 kg.

Then, we start the modal analysis simulation and in the pictures below we can see the results:

Focusing the attention on the first three vibrational modes, we can see that the first and second modes are flexural and the third mode is torsional.

Another characteristic that we want to calculate is the lateral and the torsional stiffness.

To determinate the right calculation method, we used the procedure described in V. Cossalter’s book (*Motorcycle Dynamics*).

First of all, the swingarm pivot must be locked and then we must apply a force along the wheel axle and, from the displacement resultant, we can determinate the lateral stiffness.

About the torsional stiffness we must apply a torque around the longitudinal axis and, from the rotation, we can find the result.

Typical values for the lateral stiffness are between 0.8 and 1.6 kN/mm and, for the torsional stiffness are between 1 and 2 kNm/°. The figure below shows how to calculate the lateral and the torsional stiffness.

The procedure described upon was applied at the FEM model and, using the mathematical relations *F = K·x* and *M = K·θ*, we discover that the swingarm has both stiffness in accordance to the bibliography data.

## 3. Single-sided aluminium swingarm

This particular swingarm gives to the bike a look very attractive. We can see it in lots of Italian bikes, for example: Ducati 916 (year 1994), 996, 748, 998 (year 2004) and Aprilia RS 50 (year 1998).

In the images below we can see how we have determined the mass, the center of gravity and the moment of inertia of the swingarm.

Summarizing, the properties are:

- Mass: 6.545 kg;
- Moment of inertia: [0.26, 0.21, 0.04] kgm
^{2}

In the laboratory of the MDRG Group of the University of Padova the swingarm was tested to determine the vibrational modes and the relative frequencies. The instruments used was:

- terminal anchorage
- accelerometer
- calibrated hammer
- data logger
- PC
- Acquisition software
- Elaboration software

The swingarm, previously locked at the terminal anchorage, was hit with the calibrated hammer in twenty points of it and then, with an accelerometer, the accelerations were calculated. Subsequently, with the FRF (frequency response function), the vibrational modes of the swingarm were determined using an appropriate elaboration software.

In the images below there is a summary and the animations of the first three vibrational modes of the real single-side aluminium swingarm.

Now, with the FEM software Patran the vibrational modes of the geometry model were calculated and, as we can see in the table below, there is not so much difference from the test result.

## 4. Innovative swingarm

Up here, we have seen two model, each one with a level of innovation: the first, is the model of a classical swingarm with the degree of innovation in the material used that is the carbon fiber, and a second model, a single-sided swingarm with the degree of innovation situated in the geometry.

Now, we want to combine the two degrees of innovations creating an innovative swingarm: a single sided swingarm made in carbon fiber.

The purpose of this third part of the present work is to find a correct sequence of lamination of the carbon fiber plies that allows to have the same stiffness of the aluminium swingarm but more lightweight of the original one.

For the first attempt we used the same lamination sequence of the first swingarm seen in this presentation, but the values of the stiffness were very low. Then, after a number of attempts, we obtain the correct sequence of lamination:

*[0 / 90 / +45 / -45 / +45 / -45 / 0 / 90 / 0 / 90 / +45 / -45 / 0 / 90 / 0 / 90 / +45 / -45 / +45 / -45 / 0 / 90] _{s}*

and the total thickness was 5.28 mm.

Now, we can verify that, from equation

if the stiffness K is equal, and if the mass decreases, the frequencies of vibration must increase. In fact from the fem model of the single-sided aluminium swingarm to the new model in carbon fiber the frequencies decrease about 15%. See the table below to read the values obtained.

## 5. Conclusions and future developments

This work wants to combine the models of two different real swingarm to create another one with unusual characteristics. The project considers only the vibrational aspects without considering forces and moments that may act on the bike during the acceleration, braking and cornering moments. In the future, we can study the behaviour of the innovative swingarm during the manoeuvres above and we can evaluate the critical points providing appropriate stiffeners to reinforce it.

## 6. Download

Here you can download my thesys in pdf format.

Giacomo Sarti

October 2013

Thanks for your project present a to. I want motorcycle yaw mode occurs at 70 to 100 Km ph.

How can affect torsional modes frame ,swing arm .

Regards

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