RESULTADOS POR DIMENSIÓN SOBRE LA ENCUESTA A ESTUDIANTES

The first major decision to be made regarding the tyres is which size to use. The formula student rules(13) specify that all tyres must have a diameter larger than 8’’ (20.32 cm) but in reality most teams either use 16’’ (40.64 cm) or 20’’ (50.8 cm) tyres so these were the two sizes that were considered. Tyres are typically specified in the following way: 7.2/20.0-13. All the dimensions are in inches, the first number represents width of the tyre, the second number represents the overall diameter and the third represents the diameter of the rims. There are trade-offs between using larger or smaller wheels. The main advantage of the smaller wheel is the decreased weight; it is highly desirable to save weight in this area as any rotating bodies on the car have an associated rotational moment of inertia which will slow the car during acceleration. Solidworks models of a 16’’

7.0/16.0-10 m = 3.8 kg J = 0.134 kg/m2

7.2/20.0-13 m = 4.9 kg J = 0.265 kg/m2

and 20’’ tyre, based off the specified tyre dimensions, were constructed to analyse the difference in rotational moment of inertia.

Figure 6.4.3 Solidworks models of the two tyre size options, 20’’ and 16’’

As can be seen from figure 6.4.3, the rotational moment of inertia of the 16’’ tyre is roughly half that of the 20’’ tyre. The difference between running the two tyres equates to an extra 5 Nm of torque per tyre if the car is accelerating at 1 g. But during 1 g acceleration the transmission will be outputting over 800 Nm of torque at the rear axle so it is dubious whether the smaller tyres would have that great an impact. Looking at previous teams there is a reason that the 20’’ tyre is the most popular; not only is there a greater selection and more available rims in this sizing, the larger diameter also allows lots of space within the rim for packaging the brakes and wheel hubs. For this reason the 20” tyres from Avon motorsport were selected.

6.4.3 Rim Selection

The 20’’ tyre is mounted on a 13’’ rim; it is desirable to minimise the weight of the rim to minimise associated rotational moment of inertia. There are some companies such as ‘OZ Racing’ which offer a specific wheel package for formula student teams. A summary of their two products is shown in the table below.

Table 6.4.1 Comparison of the two rims offered by ‘OZ Racing’’

OZ Aluminium Wheel OZ Magnesium-Alloy Wheel

Mass (per rim) _{3.4kg 2.45kg}

Cost (per rim) _{£183.50 £362}

Clearly there is a trade-off between the cost of the rim and the weight. Although the magnesium alloy wheel seems an attractive package, the set would cost £715 more than an aluminium set.

After discussing the topic within the team, the decision was made to use the aluminium wheel as the money saved could be better spent improving other parts of the car (for example building a carbon monocoque instead of a space frame). A Solidworks model of the aluminium wheel was built using the specifications from OZ racing and the rotational moment of inertia was found to be 0.0628 kg/m² .This data was combined with the tyre data and used in the simulation.

6.4.4 Tyre Theory

The tyres generate friction with the road in two ways: Adhesion is the tendency of rubber to stick to other materials; it is thought to be the result of momentary molecular bonding and energy is lost in breaking these bonds. Deformation occurs when rubber slides over a rough surface and the high points on the surface (asperities) penetrate the rubber. As the tyre passes over a peak, each element of the rubber experiences an increase in pressure as it is loaded (going up the peak) and then a subsequent decrease in pressure as it is unloaded (coming down the peak) The increase in pressure during the loading process is greater than the decrease during the unloading process, and the result is a net resistance (14). Both these frictional effects are incurred because of ‘slip’

between the tyre and the road surface. If the car is accelerating or decelerating, the longitudinal forces are related to the ‘longitudinal slip’ (sometimes referred to as ‘slip ratio’) as defined by:

i=V_slip

V ×100 =

(

^rωV

−1 )

^{× 100}

Where V is the linear speed of the centre of the tyre, Vslip is the average speed of the rubber within the contact area, ω is the angular speed of the tyre, r is the rolling radius of the free rolling tyre (15). A driving torque will result in a positive slip ration as rω > V and a braking torque will result in negative slip as rω < V. A pneumatic tyre will typically experience maximum tractive force at a slip of between 15% and 20% (11). Figure 6.4.4 shows how the coefficient of friction varies with the slip for a braking tyre, notice that a fully sliding tyre results in a lower coefficient of friction so wheel lock should be avoided where possible. Unfortunately, Avon does not provide data for the peak friction

coefficient of their tyres, but for the purpose of this project it will be assumed that μ = 1.2 at critical slip, this is a reasonable estimate considering the results from previous years’ cars and online research (16).

Figure 6.4.4 Relationship between longitudinal slip and coefficient of friction (under braking) (17)

So far the tyre has only been considered under loading parallel to the direction of travel, but it is also important to understand how the tyre behaves under lateral loading (in a corner). As can be seen from figure 6.4.5, under lateral loads there is tread deformation at the contact patch. As a result the rolling path of the tyre is not in line with the direction of the wheel, this angular difference is known as the ‘slip angle’. Just as with longitudinal slip, there is a critical slip angle which can sustain the greatest lateral force (greatest cornering force). For normal road going vehicles this is approximately 18° whereas for racing tyres it is around 6

ۤ

° (11). Figure 6.4.6 below shows how the available cornering force for the Avon tyres varies with different slip angles and under different loads.

-4.00

Figure 6.4.6 Plot of Cornering Force vs. Slip Angle provided by Avon Motorsport for 7.2/20-13 slick tyre at a camber angle of 0°, pressure 21 Psi and velocity 20 kph. (6)

Oversteer vs. Understeer

During a corner, a slip angle will be generated at both the front and rear tyres, if the slip angles are the same (and the front and rear are generating similar levels of grip) the car should corner

neutrally. If the slip angle at the rear is greater than angle at the front then the rear tyres will approach the ultimate grip limit first and so oversteer will occur. If the slip angle is greater at the front, the car will experience understeer. This car is rear wheel drive and so will have a tendency to over-steer due to a phenomenon known as ‘power-over-steer’. If the driver presses the throttle during the corner, extra tractive force is applied to the driving wheels. This extra tractive force increases the slip angle at the rear wheels and so promotes over-steer (19).

In document UNIVERSIDAD CÉSAR VALLEJO (página 65-85)