TECHNOLOGY – SIMULATION

Set-up referencing

The 2D tyre modelling conundrum, and how to fix it BY DANNY NOWLAN

from Stock Cars to open wheelers, and I have seen the same themes emerging. Principally, when using a 2D tyre model (traction circle radius as a function of load only) you have correlation, but the sensitivity of the model to very fine changes is extremely small. The trends still point you in the right direction, so it’s still useful, but the changes are much smaller than what you would see on an actual car. The purpose of this article is to explore why this is, and propose a simple fix for it, that I will term set-up referencing.

O

ver the last couple of months I have been involved in a number of diverse car modelling projects,

Let me add from the outset

that this is an article designed to get you thinking, not the final word on how to model a tyre. Consider this a discussion paper on the mechanisms that drive what we see when we make a set up change on a car. The crux of the 2D tyre model

is effectively determining the traction circle radius (or Pacjeka D term) as a function of load only. This can either be done from tyre test rig data or using the ChassisSim tyre force modelling toolbox. If done right, you should be looking at a correlation something like shown in figure 1. Remember, when you create

a 2D tyre model you are taking a snapshot of the tyre at a particular pressure and internal temperature condition. This is illustrated in figure 2. Where 2D models struggle is sensitivity. Let’s illustrate this with some hard numbers, in this case, from a V8 Supercar (see table 1). A representative 2D tyre model is shown in table 2. Now that we have this information, let’s explore some set up sensitivity parameters. One big change in a V8 Supercar is a rear roll centre change. Typically, 10mm will produce a measurable change. To keep things simple, let’s apply a lateral acceleration of 1.4g and use this acceleration to estimate tyre loads and

approximate cornering force. The results are shown in table 3. What is presented in table 3

is a very simplified analysis. We are simply taking a static weight and applying a load transfer to it for a typical low-speed corner. What is revealing is that while the speeds are representative and the magnitude of the change is very small. With the 10mm rear roll centre change, the tyre loads have changed by a mere 3kg, and the speed has changed by 0.2km/h. Yet, in practice on the car, you’ll typically see a change of 0.4-1km/h. The truth, then, is somewhere in the middle, but this illustrates well how a 2D model gives you a good broad brush stroke, but lacks fidelity.

January 2012 • www.racecar-engineering.com 59

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