17-08-2012, 02:38 PM
Designing Stable Three Wheeled Vehicles, With Application to Solar Powered Racing Cars
Designing Stable.pdf (Size: 541.52 KB / Downloads: 170)
INTRODUCTION
Many of the vehicles that participate in solar car racing have three wheels, arranged with two in front and one at the rear. There were some incidents in Sunrayce ’95 involving such vehicles, but also many of the top finishing cars were three wheelers. This suggests that there are probably some “do’s and don’ts” regarding the design of these cars. This paper will discuss the dynamics of three wheeled vehicles, and show how improved stability can be designed in.
Tire Response to Side Load: Slip Angle
When a loaded rolling tire is subjected to a side load, its path is deflected from the direction in which the tire is headed. The angle of deflection is called the slip angle. Figure 1A shows a top view of a tire with side force Fapplied at the axle line, with velocity V along the direction of travel, and slip angle between the actual path and the tire heading. (It is presumed the axle rotates in bearings which keep the tire vertical to the road). Figure 1B shows the front view, with lateral force F acting upon the tire from the ground, and a vertical load N, along the centerline. Lateral force F is equal in magnitude to side force F.
There is a relationship between the lateral force F and the slip angle, which is found experimentally and reported in the technical literature as plots of lateral force F vs. slip angle for various vertical loads. In that literature, the positive force direction is as indicated in Figure 1B, so force F had negative values for positive slip angle. Figure 2 shows such a plot for a 17” bicycle tire.
A tire has a maximum slip angle, above which the tire will slide. That is, if the side load F exceeds the lateral load that the tire can produce at its maximum slip angle, then the tire will slide, rather than “slip”.
Figure 2 reports data for slip angles of 3 degrees, from which it may be implied that the maximum is not much above that value. Plots for automotive tires have maximum slip angles of around 10 degrees.
WEIGHT TRANSFER IN BRAKING
For a three wheeled vehicle that has 2/3 or more of the weight on the front two wheels and a high CG, one could envision that the forward weight transfer under hard braking may severely reduce the vertical load at the rear. This could be studied as a potential yaw situation in vehicle dynamics, but in keeping with the use of simple models, a quasi-static approach will be used to determine the fraction of the static weight at the rear that is transferred to the front in braking. Figure 8 shows a side view of a vehicle under braking. It could have 3 or 4 wheels. The braking deceleration is denoted by FB as a fraction of the acceleration of gravity. The static vertical load at the front is WF and on the rear is WR. Weight transferred to the front during braking is denoted as ΔWR, which is a positive value.
CONCLUSIONS
This paper presented a tutorial treatment of elementary vehicle dynamics models in order to show how certain vehicle parameters affect vehicle stability. The concepts of slip angle, cornering stiffness, yaw response, neutral steer point, Static Margin (SM), Understeer Gradient (K) and tipping threshold were described. The “bicycle model” was introduced and its yaw response was described when subjected to both a side load while running in a straight line, and to a centrifugal force while cornering.