Summary from the thesis of Ivan Simionato, graduate in Mechanical Engineering from the University of Padua.

This works is focused on the development of a multibody model of the MG07.12 using the software ‘LMS Virtual Lab’. It will be used to define the optimal setup of the car for a specific track, verifying the results with a data acquisition system on the real vehicle.

## INTRODUCTION

The MG07.12 involved in this paper is the single-seater car built by RaceUP Team (www.raceup.net) to compete in Formula SAE events (http://students.sae.org/competitions/formulaseries/) for 2012 season.

A Multibody model of the vehicle was previously developed by F.Cagnin in his thesis “Multibody analysis of the Formula SAE car MG0712” (link).

## PURPOSES

The purposes of this work are:

- Enhancing the multibody model adding new parts and removing some approximations of the old one.
- Finding the best setup for the “skidpad” event, launching several multibody analysis and changing each time a single parameter in order to find the best value. The controlled parameters are: camber, toe angle, antiroll bars, springs and also the front and rear track of the vehicle.
- Adding new informations to the multibody model thanks to some laboratory measurement made on the vehicle.
- Comparing the response of the model with the real vehicle, making a test on track with a data acquisition system on it.

## SKIDPAD LAYOUT

Formula SAE competitions are composed of various static and dynamic events: among the last ones, the skidpad competition will be in particular analyzed in this work. The skidpad track is an official FSAE event. It’s a well-defined track “8-shaped” to travel in the lower possible time, in which chassis and dynamic characteristics of the vehicle are tested.

## MODEL IMPROVEMENT

The old model had a rigid rod connecting the two rear wheels. A self-locking differential model was still available, thanks to a project by I.Simionato and G.Sottana (link), and it was imported in the model.

Suspensions have been made completely parametric, removing every solid part and using only distance constraints, but maintaining the cinematic properties. The distance values were then imported in a single and simply-editable Excel file, making setup changes very fast.

Antiroll bars geometries, approximated in the old model, were adjusted referring to the real vehicle. The torsional stiffness of the available bars was also calculated, since only a qualitative value was used before.

## OPTIMAL SKIDPAD SETUP

Starting from a basic setup, each parameter (camber, toe, antiroll bars, springs and vehicle tracks) was singularly changed in this order. Simulations were made on the “skidpad” track, with a steer control and constant rotational speed of the rear sprocket, improved till the limit grip conditions for each analysis. For example, various simulations were launched changing only the camber angle, in order to find its optimal value. Once done this, the optimal value was kept, and a new group of simulations was launched changing toe angle, and so on. In the end, a complete and optimal setup configuration was obtained for the “skidpad” event.

## MEASUREMENTS

Some measurements were made on the vehicle, in order to improve even more the model definition:

### CoG Position

Dampers were substituted by rigid elements of equivalent dimensions and weight. The vehicle was weighted on four electronic balances, in order to find the center of gravity (COG) location on XY plane. The vehicle was then inclined to one side till the equilibrium, measuring the inclination angle in order to find the COG position on Z axis, thanks to some geometrical considerations.

### Moments of Inertia

The car was then put on a specific measurement machine in order to define the Moment of Inertia Tensor. This machine is elastically suspended, and offers 3 dof (roll, yaw, pitch) which can be combined in various ways. Inducing an oscillation, the main oscillation frequency is measured, and thanks to an existing calculation code, the matrix of the moment of inertia tensor is calculated.

### Antiroll bars torsional stiffness

A last measurement was made on the antiroll bars, to verify the estimated torsional stiffness. After a proper constraining, leaving free only the torsion of the bar, the free side was loaded, and its displacement measured with a comparator, in order to calculate the torsional deformation and so the torsional stiffness. The values previously estimated were found to be enough accurate.

## TRACK TEST

The vehicle was equipped with a “2D Datarecording” data acquisition system, fitted with the following sensors:

- Inertial platform (triaxial accelerometer and gyrometer)
- GPS antenna
- Linear displacement sensors on each suspension
- Rotational displacement sensor on steer column
- RPM sensor on rear sprocket

The definitive test wash held on Istrana Military Airport (TV) on 7/6/2013. Five skidpad attempts were registered, and the best of them used as comparison with the model.

## COMPARISON BETWEEN MODEL AND REALITY

The real event was recreated in the multibody software: signals of steer angle and rear sprocket RPM acquired on track were used (properly filtered) as input in the LMS model, also fitted with the same setup of the real car. The simulation was launched with those conditions, and compared to the real vehicle acquisition. For some acquisitions, a properly designed Kalman filter was used to remove the noise and correct some readings. In particular considering the position of the inertial platform, positioned away from the COG of the vehicle.

The comparison was made in term of:

- Lateral acceleration
- Linear sensors displacement
- Roll angle
- Sideslip angle
- Vehicle speed
- Yaw rate

## CONCLUSIONS

The model response is completely comparable to the real behavior of the vehicle for nearly every considered parameter. Only the sideslip angle wasn’t fully comparable, because it was obtained by an estimation from the Kalman filter and not directly measured as the other parameters. A little delay of the simulation signal is notable, especially during the direction change, compared to the real vehicle signal. This is probably due to the infinite rigidity of the chassis in the model, while the real vehicle has a finite-rigidity chassis. The optimal setup found exclusively with the simulations was also very similar to the one obtained following driver’s indication on the track.This means that the model is very representative of the real vehicle, and that it responds very well to setup changes.