Plotting Cn-Cy and Cn-Ay Graphs.

[apoorv]

Hello this is Devansh from Srm university,chennai. I am working on vehicle dynamics for our 2nd vehicle for FSAE 2016. We have been plotting force moment diagrams for our vehicle. We first created Cn-Cy diagram on Matlab in which for each delta and beta ranging from -5 to 5 in steps of 0.5 we iterated Ay based on slip angles and verticle loads (considering lateral load transfer with new Ay for each iteration). All the Fy data was imported from pacejka tire model.In Cn-Cy Ax=0.2

Then we plotted Cn-Ay in which we first assumed intial yaw rate and iterated yaw rate along with Ay similar to Cn-Cy but this time slip angles were calculated for each iteration(as yaw rate varies).

The Cn-Ay and Cn-Cy graphs looked almost similar. The constant steer lines of Cn-Ay are intersecting 0 yaw moment(Cn=0) line almost at max acceleration. Which makes this graph similar to Cn-Cy.Even when I change my CG location close to front axle in both the graphs the lines now intersect Cn=o before max Acc. which again makes both the graphs look similar.

I guess my understanding of the difference between Cn-Cy and Cn-Ay is not fully clear. In RCVD its mentioned that the most significant difference between Cn-Cy diagrams and Cn-Ay diagrams is that in Cn-Cy the total lateral force generated is not assumed to resist the acceleration of the vehicle mass. Instead, some portion could be used to resist an outside disturbance. whereas in Cn-Ay all lateral force created by the tires is used to hold the vehicle in steady state equilibrium without any outside disturbances.

Does this difference b/w the 2 diagrams change the way in which Ay iterations are done? Am I missing something or this behaviour of graph is acceptable?

I have attached respective images of the plotted graphsCn-Cy.jpgCn-Ay.jpgCn-Cy cg front.jpgCn-Ay cg front.jpg

[Adam Farabaugh]

The difference:

CN-Ay
- all lateral force goes to lateral acceleration
- diagrams are typically drawn at constant velocity
- thus since velocity is known, and lateral acceleration is known, radius is known
- note that instantaneous radius varies across the plot
- can also do this with constant yaw rate

CN-Cy
- some lateral force may not go to lateral acceleration
- for this reason it's possible to generate the plot at a constant radius
- this diagram should be asymmetric, since negative lateral acceleration on a positive radius is different than positive lateral acceleration on a positive radius


Looks like you have some problems, your CN-Ay is not totally symmetric, also the zero beta/delta point is not on the origin for some of your plots. Is the car setup symmetric?

[Claude Rouelle]

Devansh,

This is not answering your question but here is an observation: there are no legend on your graphs so we do not know what the values of the beta and delta isolines of your graphs are.

In any case, as Adam just mentioned, it seems that the isolines of beta = 0 and delta = 0 are not crossing at the graph origin of coordinates CN = 0 and Ay = 0

If you car is symmetrical and you are going straight (beta = 0) and you do not have any steering input (delta = 0) you can't have any yaw moment or any yaw acceleration.

When students try to create a yaw moment Vs Lateral acceleration graph 99% of them face this issue. If you want a hint, have a look at your tire and car system of coordinates.... You cannot look the whole car and the tires in 2 different systems of coordinates.

[apoorv]

Sir, we followed your advice and multiplied the lateral forces(Fy) at the rear by cosine of the body slip angle(beta) and then multiplied the front tire lateral forces by both the cosine of steer angles(delta) and cosine of body slip angles (beta) to change them in velocity frame coordinates which is aligned at Beta to the vehicle axis system.

So my "Fynew at rear" = Fy*cos(beta) and "Fynew at front" = Fy*cos(beta)*cos(delta).

But still my Cn-Ay graph look similar to the previous graphs as the constant Beta=0 and constant delta=0 lines are not intersecting at the origin. In the attachment below Z=0 is the constant beta line intersecting the constant steer line = 0 at Cn=0 and Ay around 0.24(both are Cn-Ay). So I still am confused as to how, despite of factors such as conicity and plysteer these lines would intersect at the origin.

Have i changed the coordinates correctly? Am i missing something else here? Should converting coordinate system give Ay=0 or not? Is it the solution to my previous problem? CnAy close to Nsp velocity coordinate.jpgCnAy front velocity coordinate.jpg

[Adam Farabaugh]

What is the output of your tire model at zero slip angle at various loads?

What other effects are you modeling? Inclination angle? Ackerman? Change of inclination with ride and steer? Compliances? Hard to tell what the problem is without knowing how complicated your model is. Would suggest that if you do have any of these things modeled you turn them off until you can get symmetry with the simplest possible model (tire model + weight transfer)

[apoorv]

At zero slip angle tire is producing some lateral force. The inclination angle is 0, no ackerman, no compliances. The minimum slip angle in the lookup table exported from tire data is +0.0502 and -0.0502 which matches with 0 slip angle in matlab calculations. Can this be the cause of asymmetry ?

[Claude Rouelle]

Devansh,

Let me repeat the same thing but with other words.

No tire is perfectly symmetrical. Even with no slip angle and no camber it could be that your tire will produce a side force. OK, now imagine your beta and delta are both = 0 and your car has a symmetrical setup (in other words you are in straight line) and you have no camber and not toe. If in these conditions, your LF tire and RF tires both pull a force in the same direction (pulling the car to the left of the right) there will be a lateral acceleration and most probably a yaw moment (unless your weight distribution is exactly 50-50 and you have exactly the same front and rear tires and a=b). Something is wrong....

Most of the time students do not adapt their tire coordinates system to the chassis coordinate system. I remember having clearly explained this in the last seminars I taught for at least the last 5 years.

Is this helping or not?

[Adam Farabaugh]

Hint at the solution, look in the mirror (while holding a plot of lateral force vs slip angle)

[BillCobb]

Instead of trying to use a model which has a hint of extra complexity, try creating a simple tire model formulation using a 2 term exponential slip sensitivity and a linear load sensitivity. Once that seems to be working go ahead and add some nonlinear load sensitivity.

If all that makes sense, add the aligning moments and perhaps some non-zero slip responses. After that, you can open the throttle with some real tire data.

[Claude Rouelle]

Nice and simple way to present the perspective (literally!) Adam.

In the seminar I show it with another visual trick: in the Adapted SAE tire coordinate convention system, I take the graph the RF tire Vs its slip angle then flip it once around the X axis (slip angle axis) and then one more time around the Y axis (force axis). From there you see the 2 side forces at 0 slip angle are in opposite direction and there ore no resulting chassis lateral force in a straight lime.