Pneumatic Tyre Characteristics

Introduction
The purpose of this technical report is to communicate the results of the Pneumatic Tyre Characteristics laboratory by investigating the effect of cornering force on slip angle. The technical report is presented to the academic staff of the Engineering Systems Department at the Royal Military College of Science, Shrivenham. It is assumed that the reader is fully familiar with the experiment and with the equipment on which it is preformed.

Experimental Conditions
• For this particular experiment the gain of the output for the strain gauges are set to 1 as 0 to 8 degrees slip angle is been measured. If smaller angles are measured a larger gain may be required.

• The total displacement of the trolley that runs along the track is approximately 2.17 meters. However, this may slightly vary in the results, especially with higher slip angles due to the reaction force acting on the reversible hydraulic motor that drives the track. For consistency the corresponding point for each distance is taken in the results.

• The current details and condition of the tested tyre are given.
- Manufacture: Avon.
- Dimension: 710 / 22.0 – 13.
- Condition: Generally worn all around with patches of the tyre (approximately 60mm in diameter) in worse condition on the inside of the wheel.

• The tyre was tested at 14, 16 and 18 psi pressure. For each test at each angle increment the air valve is pointing downwards purely for consistency as the tyres circumference may vary. The increments for each test are as follows.
- 0 – 5 degrees in 0.25 degree increments.
- 5 – 8 degrees in 0.5 degree increments.

• The experimental equipment is set to output 1000 points of displacement and side force. The computer capture rate is set to 50Hz and a total run time of 20sec

• Final experimental conditions that should be mentioned include:
- Before the conduction of the experiment the camber of the wheel should be checked and adjusted to zero degrees.
- The track is manufactured to have a sand paper surface. This is important to exert a sufficient side force on the tyre and is in good condition.
- For each experiment, initially slip pads are used under the wheel as the mechanical mechanism used to apply the vertical force is applied at a radius and therefore would give an unwanted offset.
- A constant vertical load of 1.5kN is applied to the tyre. This load is kept consistent by a mechanism which includes a beam and counter balance weights.

Experimental Results

The experimental results are outlined below.

The calibration factors given are:
- Displacement trackway 0.655 m/volt.
- Side Force 1.89 kN/volt with -0.07v being 0kN.

Figures 1, 2 and 3 below show the cornering force versus displacement along the track for 14, 16 and 18 psi respectively.

Figure 1

Figure 2

Figure 3

Figure 4 below shows the cornering force versus the slip angle for 14, 16 and 18 psi at 1.4 meters along the track. The tabulated data is shown in appendix 1.

Figure 4

Figure 5 shows the coefficient of friction versus the slip angle for 14, 16 and 18 psi. The tabulated data is shown in appendix 2.

Figure 5

Figure 6 shows experimental data from Milliken and Milliken [1]

Figure 6

Observations and Discussion

Figures 1, 2 and 3 show the cornering force versus displacement along the track for 14, 16 and 18 psi respectively. The graphs are achieved using Microsoft Excel with the calibration factors and offset accounted for. Figure 4 shows the cornering force versus the slip angle for 14, 16 and 18 psi at 1.4 meters along the track. The general trend for each psi show that as the slip angle is increased the lateral force is increased. The elastic, transitional and frictional changes can be seen. The peaks of the curves remain roughly constant and slowly begin to fall off. The transitional range for the 18 psi extends over a sizable slip angle range as opposed to being more abrupt for 14 psi. The latter would tend to give little warning and would tend to let go suddenly.

From graphs 1, 2 and 3 there seams to be strange behaviour at 1.5 meters for each psi. Due to this, figure 4 takes the measured cornering force at 1.4 meters where the results are more reliable. Figure 4 could also be achieved by averaging the force between say 1.3 to 1.5 meters to get similar results. The reason for the strange behaviour after 1.5 meters could possible be due to damage to the tyre or to the track. The most likely cause could possible be due to grease from the slip pads getting onto the wheel. This would explain the large reduction in cornering force. To isolate this problem and be convinced of its effects would require more experimentation e.g. Start the tire at a different place by maybe placing the tire so that the valve is vertical.

Figure 5 shows the coefficient of friction versus the slip angle. This concept of friction coefficient is defined as:

The normal force is known and is applied at 1.5 kN. The frictional force is taken at 1.4 meters along the track. The tire at 18 psi has the highest friction coefficient so would tend to let go faster as more of the tire print has been utilised for elastic distortion.

Finally figure 6 shows the experimental results from Milliken and Milliken. This is shown to give a representation of the expected results. In this case it can be seen that the slope of the cornering force curve falls off rapidly with increase in traction ratio.

It should be noted that the quality of the results are not very accurate and some of the sources of the experimental error may be from:
1. The quality of the tire and track conditions are not in particularly good condition.
2. There may be faults in the experimental equipment and may cause movement in the trackway.

Conclusions

The following conclusions may be found:
• The information from the results could be improved in terms of accuracy if multiple tire samples were taken. This would also help reinforce the above results. The tire temperature could also be controlled and monitored for consistency.
• From the results in general it can be seen that the increasing slip angle increases the lateral force linearly through the elastic region and then the force reduces as it goes through the transitional phase.
• The peak lateral forces acting on the tire increase with the increasing tyre pressure.
• The experimental errors have greatly affected the end results and hence produced what appears to be a lot of noise.

References

1. Race Car Vehicle Dynamics – Milliken & Milliken – Society of Automotive Engineers International, Inc. – 1995

2. MEM 4 – Motorsport Vehicle Dynamics Course Notes – 2005 – MSc Motorsport Engineering & Management – Cranfield University

Appendix

Appendix 1

Slip Angle (Degrees) Force KN (14 psi) Force KN (16 psi) Force KN (18 psi)
0 0.02617207 0.021557813 0.035400586
0.25 0.261499219 0.27995625 0.266113477
0.5 0.446069531 0.436841016 0.446069531
0.75 0.598340039 0.644482617 0.630639844
1 0.801367383 0.847509961 0.833667188
1.25 0.893652539 0.995166211 0.97670918
1.5 1.009008984 1.128979688 1.096679883
1.75 1.110522656 1.262793164 1.225879102
2 1.133593945 1.373535352 1.327392773
2.25 1.244336133 1.41967793 1.387378125
2.5 1.258178906 1.50273457 1.438134961
2.75 1.244336133 1.525805859 1.470434766
3 1.258178906 1.576562695 1.507348828
3.25 1.20742207 1.571948438 1.539648633
3.5 1.31355 1.56733418 1.558105664
3.75 1.308935742 1.562719922 1.56733418
4 1.332007031 1.576562695 1.585791211
4.25 1.332007031 1.655005078
4.5 1.332007031 1.571948438 1.682690625
4.75 1.322778516 1.664233594
5 1.350464063 1.539648633 1.521191602
5.5 1.415063672 1.576562695 1.516577344
6 1.373535352 1.571948438 1.539648633
6.5 1.336621289 1.581176953 1.581176953
7 1.373535352 1.516577344 1.585791211
7.5 1.410449414 1.507348828 1.6088625
8 1.373535352 1.516577344 1.585791211

Appendix 2

Slip Angle (Degrees) Co-Efficient Friction (14 psi) Co-Efficient Friction (16 psi) Co-Efficient Friction (18 psi)
0 0.017448047 0.014371875 0.023600391
0.25 0.174332813 0.1866375 0.177408984
0.5 0.297379688 0.291227344 0.297379688
0.75 0.398893359 0.429655078 0.420426563
1 0.534244922 0.565006641 0.555778125
1.25 0.595768359 0.663444141 0.651139453
1.5 0.672672656 0.752653125 0.731119922
1.75 0.740348438 0.841862109 0.817252734
2 0.755729297 0.915690234 0.884928516
2.25 0.829557422 0.946451953 0.92491875
2.5 0.838785938 1.001823047 0.958756641
2.75 0.829557422 1.017203906 0.980289844
3 0.838785938 1.051041797 1.004899219
3.25 0.804948047 1.047965625 1.026432422
3.5 0.8757 1.044889453 1.038737109
3.75 0.872623828 1.041813281 1.044889453
4 0.888004688 1.051041797 1.057194141
4.25 0.888004688 1.103336719
4.5 0.888004688 1.047965625 1.12179375
4.75 0.881852344 1.109489063
5 0.900309375 1.026432422 1.014127734
5.5 0.943375781 1.051041797 1.011051563
6 0.915690234 1.047965625 1.026432422
6.5 0.891080859 1.054117969 1.054117969
7 0.915690234 1.011051563 1.057194141
7.5 0.940299609 1.004899219 1.072575
8 0.915690234 1.011051563 1.057194141