Confusing Steady State Simulation output

[Vishwajeet]

Hello,
My name is Vishwajeet Karmarkar and i am part of Stes Racing, a team based in pune,India.
I have a few questions regarding the output of a steady state simulation i am running.The aim of this simulation is to find the steering angles at the inner and outer
wheels so as to finalize the steering geometry.
What i am doing is as follows.(working in matlab)
I first assume a certain value of lateral acceleration, and cornering radius.Based on this i find the vehicle velocity.Then i find the normal force on each tires for that
acceleration.I give the program a inner wheel steering angle input(which is closer to the ackerman steering angle).Then I iterate it for multiple values of B(body slipangle).For the current B, the program finds the slip angles at rear inner and outer wheels, as well as front inner wheels(eqs from chapter 5 RCVD).For these slip angles, and the tire loads, i run an optimum t matlab add in to get the lateral force generated by each tire.Subtracting the sum of these three lateral forces
(front inner, rear inner ,rear outer) from the total lateral force required(mass X lateral accln) i get the tire force which should be generated by the front outer wheel.Then based on this value of lateral force, i find the slip angle on the front outer wheel, again using optimum t add in.Then i put this value of slip angle in the RCVD eqn which relates steering angle, B and slip angle, to get the value of steering angle at the outer wheel.

I keep iterating this for multiple B, until i get the lowest value of yaw moment.I also consider the Mz contributed by the tires in this simulation.
So the code keeps iterating until the lowest value of yaw moment(closer to neutral steer) is found, and at the lowest value it gives me the steering angle at the
outer wheel.

My results are however a bit strange.At lower steering values i get an anti ackerman geometry and at bigger steering angles i get a pro ackerman geometry.

Heres the result at 1.3g cornering.
Inner=[1.799 2.3259 5.1408 8.721 10.9661 22.4883 33.7706]
Outer=[3.8123 4.1171 5.3421 6.9216 7.8891 12.6199 16.8906]

So my question is whether the process i am running is flawed in some ways?If not is the steering geometry i am getting possible to implement?Also the outer wheel turns so less which makes me feel its wrong somewhere

Thank You.
Vishwajeet Karmarkar
STES Racing

[DougMilliken]

What is the corresponding speed and turn radius for each of your seven cases?

[Vishwajeet]

Radius=[70 50 20 11.5 9.125 4.5 3] m
Speed=[29.87825 25.25173 15.9706 12.11031 10.78754 7.57552 6.185386] m/s

[DougMilliken]

Wheel loads for each case?

To see what is going on visually, I suggest moving to CAD. Draw the car on each radius showing the slip angles for all four tires. In a different color, overplot the low speed Ackermann case on each radius -- a four-tire version of RCVD Fig 5.44.

[JT A.]

I think you should first step back and ask yourself "What is the purpose of doing this?"

There are so many parameters that can be used to balance the car. Air pressure, weight distribution, camber, springs/ARBs and load transfer distribution, etc.

Why have you chosen Ackerman as the parameter you want to adjust to to get the yaw moment to equal zero, instead of any of the other adjustments you could make to the car?

Why not choose Ackerman to maximize the yaw moment instead? Or maximise the lateral force of the front pair of wheels? Isn't that the purpose of the steering system, to make the car turn?

Then once you've done that, you can study how to improve the lateral force of the rear tires enough to achieve a neutral handling car. Then you've improved the lateral acceleration capability of the whole car!

The approach you've taken is to arbitrarily choose a lateral acceleration, and then solve for the loads an slip angles required to achieve it. Why did you choose that approach, instead of another? For example, instead of choosing a lateral acceleration and solving for the slip angles, you could work in the opposite direction. Choose steering and vehicle sideslip angles (delta and beta from RCVD terminology) and solve for the lateral acceleration. Then you could find the values of ackerman (or camber, or weight distribution, or any other parameter) that maximizes your lateral acceleration, which is one of the most important goals of a race car.

I think what you're doing now is a good conceptual exercise, but if your purpose is to design a faster race car your efforts may be a little misguided. Your simulation can only give you helpful results if you're asking the right questions out of it.

[Vishwajeet]

The first thing i was doing was trying to maximize the cornering forces from the front tires.However what i found was if i maximize the front tires lateral force, there isnt't a lot left for the rear wheels to contribute.Lets just say that 4000N is the total lateral force required(for a given cornering accln), then i found that if i maximize the front forces(assume that they contribute 2500 ) then the rear wheels wont operate at their maximum as they can only contribute 1500n.Given the fact that the rear wheels are loaded more i thought this wont be the actual case.In fact the assumption that assigning the slip angles for maximum lateral force to the front wheels didnt bode so well with me because how can i assign slip angles to tires?They depend on actual dynamic conditions dont they.In short i discovered that all four wheels cannot be operated at their maximum slip angles, and thus i had to find the spot where all four wheels are contributing to the force,and also to the neutral steer condition.
Because of the reasoning above i chose the approach i chose.
Also i am not solving for slip angles to achieve the required accln.What i am doing is giving the program an input of delta(front inner) Corner radius, velocity.And it iterates through multiple beta.So i find slip angles on the front inner, the rear inner and the rear outer, based on the rcvd equations relating delta beta and alpha.Then for these slip angles i find the lateral force for each of these three wheels.Then i get the lateral force which should be contributed by the fourth remaining wheel, i.e front outer.By finding the slip angle at this lateral force, and using the same eqn,albeit this time not for alpha but for delta, i get delta outer.

[Vishwajeet]

Ok so on reading my own answer i have discovered that the logics flawed.I assume the RCVD eqns to get slip angles for 3 tires, and for the fourth tire i use something different.What i find is that the slip angle generated by the program for the fourth tire does not match with what i would have got if i had put it in that eqn.So now i realize i spent a lot of time trying to achieve nothing.

[DougMilliken]

Might be time to re-read the introduction to RCVD Chapter 8.

When Bill (my father) worked out the first points and drew a simple MMM diagram in the 1960s, it took over a month to run the computations with a paper spreadsheet and a slide rule.

Powerful tools (like Matlab) let you make mistakes faster!

[BillCobb]

Take a look at this thread in the TTC Forum Subsection:

"Example Simulation Using Nonlinear Tire Data"

It is not difficult to install a single input, multiple output function (SIMO) into this model that represents two steered road wheels as a function of a steering wheel input. Given several Ackermann proposals, the optimum function can (theoretically) be demonstrated.

I suggest this method because its likely that you can or should verify the accuracy and validity of your results by means of a simple road test run using some basic test instrumentation when you car appears in hardware form

A constant radius test is an alternative maneuver, also easily verified by a simple test procedure requiring little driver skill.