## Introduction

The aim of this work was to get a reliable estimate of loads acting on wheels of a kart during a track session.

The will of reaching this objective is due essentially to:

- availability of only a few data on technical literature, derived, generally, by means of numerical multibody analyses
- absence of technical solutions for direct wheel loads measurement
- this type of vehicles hasn’t any suspensions system: this brings to impulsive loads on chassis

The work was performed through these tasks:

- Conception and development of a measurement system for lateral and vertical loads on front wheels
- Making of appropriate changes to front wheel supports, in order to make possible the bonding of strain gauges
- Making, installation on the kart and calibration of the measurement system
- Estimation of the measurement uncertainty due to tyre’s deformations, using FEM analyses
- On track data acquisition
- Data analysis and final considerations

**Conception of the measurement system**

Due to the absence of a braking system on front wheels, only lateral and vertical loads can act on them. So the choice was to measure the bending moment and shear on the cylindrical beams carrying the wheels, as illustrated in next figure:

Where, as known, the slope of the bending moment diagram is equal to the shear (due to the vertical force, in this case) acting on the beam. This structural behavior has brought to the decision to develop two measurement channels:

*“Vertical Channel”*, full Wheatstone bridge, sensitive to shear*“Lateral Channel”*, half Wheatstone bridge, sensitive to bending moment

The bonding location of the strain gauges, for each channel, is illustrated in the next two figures:

With this disposition, the vertical channel is sensitive only to the vertical force and, moreover, is fully insensitive to center of pressure’s position.

Slightly different is the behavior of the lateral channel; infact, this channel is sensible to both vertical and lateral loads, and brings to a coupling of the two signals.

This problem is overcome using a calibration matrix, whose inversion gives the input-output law used to obtain force values starting from signals coming from strain gauges. It’s possible to calculate the theoretical matrix, obtaining:

**Changes to the front wheels supports**

The chosen location for bonding the strain gauges was, initially, engaged by five ring-shape spacers.

In order to make possible the bonding of sensors, it was necessary to design a special spacer, with these design constraints:

- possibility to be mounted and unmounted without damaging the strain gauges
- high flexional flexibility, in order to not absorbe flexional loads (to be measured with the half bridge mounted on the beam)
- sufficient structural strenght, in order to sustain the lateral force in a reliable way

These constraints have led to model the following device:

which can be mounted without any trouble on the wheel support equipped with strain gauges:

The spacer was, obviously, subjected to structural verifies. In particular, it was performed a strenght verification using Von Mises Criterion:

And an eulerian, buckling verification:

**Measurement system: installation on the kart and calibration**

The kart was equipped with two distinct measurement systems:

*2D-Datarecording*system, providing GPS and tri-axial accelerometer and gyrometer*IMC-Cronos PL2*system, providing Wheatstone’s bridges interface and tri-axial accelerometer

The syncronization between the systems was reached during post-processing, using signals coming from accelerometers and a trigger event, such as an impulsive braking maneuver.

The calibration was performed using some known masses, acting as loads due to gravity, with the aid offered by some pulleys, as visible in the figure, respectively for vertical and lateral loads:

The process led to two couples of calibration curves for each wheel. For example, the left wheel gave:

Whose corresponding calibration matrix is:

really similar to the theoretical one.

**Measurement uncertainty due to tyre’s deformations**

Forces acting on wheels during a track session, don’t explicit themselves just through a point, but through the birth of a contact patch between tyre and ground. Within the contact patch exists a variable pressure distribution and, as consequence, a variable position of the center of pressure. This means that the point of application of forces may move itself.

This behavior doesn’t affect the measure of shear, that is, the values coming from vertical channel. Nevertheless, it may affect in a significant way the measure of bending moment, that is, the values coming from lateral channel, because they strictly depend by the moment arm of vertical force.

The consequent measure uncertainty quantification was performed through some FEM analyses: firstly, to quantify the roll angle of the vehicle; secondly, to quantify the displacement of the center of pressure inside the contact patch.

The finite element model employed for these analyses is based on some assumptions:

- linear, elastic, isotropic materials involved
- contact modeling
- steady state
- cubic shape functions, brick elements

And is reported in the figure:

The displacement of the center of pressure is the result of two distinct effects:

- variations of camber, due to roll angle
- tyre lateral deflection, due to lateral force

Although the estimated roll angle is rather low (0.224°), its effect is not negligible, making the COP move of UX=5.59mm. The effect of lateral force is most evident, giving a deformed shape like the one in figure:

It’s possible to calculate that these effects give an uncertainty equal to, at most, 8.17% in the measure of lateral force.

The measure of the vertical force, instead, is not interested by tyre flexibility.

**On track data acquisition**

Test sessions were performed at Jesolo’s “Pista Azzurra” race track. Although weather conditions weren’t optimal (very low temperature and wet areas on the track), mined data were meaningful.

Fastest lap was completed in 55.43s, and its trajectory is visible in the next figure:

The measure of front wheel loads has been consistent with the expectations. Before giving an example of acquisition, let’s take a look to the conventions used while generating force and acceleration plots:

An example of acquisition is that taken in turn number eight:

- a straight section, where right and left loads are similar and lateral acceleration is near zero
- a right cornering beginning, where left wheel loads rise and right wheel’s get down
- a steady state cornering, where loads remain approximately constants
- a change in direction, where all values change their sign

**Conclusions**

In this work, a system for the measure of front wheel loads of a 125cc racing kart was designed. Furthermore:

- a spacer to make possible the bonding of strain gauges was designed
- the uncertainty due to tyre’s deflections was estimated to be less than 8.17%
- it’s possible to estimate loads acting on rear wheels, starting from collected data