moment diagram with weight transfer

[slicktop]

Hello,
My question is regarding the unbalanced forces and moments created when considering weight transfer. In order to obtain the required normal forces for the analysis at each tire, an input lateral acceleration must be applied. However, when the resulting tire lateral forces are computed (using Pacedjka 2002 in my case) for a given steer, body slip angle and turn radius and then moved to the cg in the direction of the turn center along with the addition of moments, the resulting force can be much less or much more than the initial applied force that was used to compute the weight transfer.

I am having a tough time wrapping my head around the above scenario. Only when the computed lateral force and the applied lateral force at the cg are equal, along with a yaw moment about the cg of 0, will the vehicle be in steady state?

It seems that the unbalanced lateral force that is computed at the cg creates a snapshot of whether that unbalanced lateral force at the cg is tending to increase or decrease the radius of the turn? Or am I way off here with my insight and approach?

If anyone has some insight on MMM diagrams with weight transfer, it would be greatly appreciated.

[DougMilliken]

RCVD Chapter 8. As a guess, you might want to study Table 8.4?

Before Claude has a chance...who are you and where are you from?

[Claude Rouelle]

Doug,

You got me me by 3 minutes! I was about to clock on "Post Now"

So here is Doug echo: Slcktop.... who are you....?

[slicktop]

Doug,
Thanks for the response. I have read chapter 8, maybe I have missed something and need to review, but I don't see where there is information about this difference in lateral force when computed as I have stated above. Perhaps there is an alternative method? I don't see how you could get around it as you have to have a weight transfer calculation first, and this leads to an unbalanced force. It seems that the graphs in chapter 8, don't show this unbalanced force.

*edit*
It seems the graphs are focused only on the unbalanced moments.

*edit #2*
It looks like i'm dealing with case #3 in table 8.4. Cn-Cy, Finite Radius, Road Load. Although, I am not sure what is meant by "Cy=Ay, where Ay produced by speed change on constant radius" Any change in speed changes my input Ay, which changes my weight transfer and tire lateral forces,etc.

[OptimumG]

Brian, I believe we spoke about this a little a bit at FSAE-Nebraska.

The typical process of solving a given combination of beta (body slip angle) and delta (steering angle) for a fixed vehicle speed involves an iterative approach. A each point of the diagram you'll hold beta, delta and speed constant, and then iteratively solve for the lateral acceleration and the yaw moment acting at the vehicle cg.

As you mention, after the first iteration, the input lateral acceleration you started with and the sum of the lateral forces from the tyres will not match. This is when you would reiterate over the problem, using the calculated sum of the tyre forces as the input for the next step. After a few iterations there should be a very small difference between the two values, at which point you can call it converged and move on to the next point.

There are various numerical optimisation algorithms that can be implemented to reduce the number of iterations required, and even though the maths (or the name of whatever function you are calling) will change depending on your chosen method, the general process won't.

(As well as updating the weight transfer calculations within each iteration, be sure to update tyre slip angles as the yaw rate will change with each new lateral acceleration, as well as updating the rest of vehicle kinematics (camber, bump/roll steer etc).

I believe I have some slides on hand from the OptimumG seminars which cover this in further detail - if you are interested and have not yet been to a seminar, I can put them up here as well as some further examples.


--
Pete Ringwood
Research & Development Engineer

OptimumG
8801 E. Hampden Avenue, Suite 210
Denver, Colorado 80231 USA
+1 303 752 1562

pete.ringwood@optimumg.com
www.optimumg.com www.optimumg.com

[Tiago_Campagnolo]

Pete,

I am very interested about this subject as well as further examples that you may have.

If possible, could you please share them with us?

The Moment Method is valuable and interesting tool and I want to create the diagram of our car too.

Thank you in advance.

Tiago Campagnolo

[Claude Rouelle]

Iago

Race Car Vehicle Dynamics book from Doug Milliken is your #1 source.

The OptimumG seminar is another one.

[slicktop]

Pete,
Yes, we did speak a bit about this subject at Lincoln. Thanks for the response - it was exactly the piece of the puzzle I was missing.

[Viv]

Hi everyone. My name is Vivek and I am the suspension lead from the University of Toronto team. I attended Mr. Claude's seminar in Indianapolis where I learnt further details about the yaw moment diagram and have also read chapter 8 from Mr. Milliken's textbook. I have since spent hours programming excel to create yaw moment diagrams for constant radius turns. It uses pacejka models fitted to TTC tire data, ride/roll camber and toe, ackermann steering, and weight transfer. I am however having problems getting the zero yaw moment at max lateral g even after adjusting various vehicle parameters. Currently the vehicle understeers at max lat g.

Pardon my ignorance if this question is trivial but I am wondering if it is truly possible to attain zero (or close to zero) yaw moment at max lat g outside the theoretical world with all these effects accounted for or is there something I am doing wrong with my program. One reason I believe I might be getting these results are because of slight asymmetry in tire data lateral forces (left turn vs right turn). Also the yaw moment at max lat g currently sits at around -500 Nm at lat g of approx 2. I also have little intuition as to how big an effect such a yaw moment would I have (which I suppose really depends on the yaw inertia of the vehicle) and if it is worth spending further hours on the issue considering this is not even the full picture considering compliance, tire aligning moments, etc.

[Claude Rouelle]

Viv,

Do you have the isoline CG slip angle Beta = 0 and the isoline of the steering angle Delta= 0 crossing the origin of the coordinates (Yaw Moment = 0 and Lateral Acceleration = 0) ?