front and rear slip angles

[Seb]

Hi,
We were facing problem in deciding the slip angles of the inner and outer tires at which we would want them to operate for extracting the maximum lateral force during cornering with the limitations we have.
With the maximum chassis roll limited to 2.4 deg (by the suspension team )during cornering the maximum lateral acceleration we can generate is 1.4g which limits our maximum lateral force to 4527 N.
the Hoosier tires 20.5*7.0 which we use peaks at around 7 deg in an Fy vs SA graph(with co-efficient of friction 0.7). Now the problem is we are not in a position to extract the best lateral force that can be generated by (due to chassis roll limitation) our tires ,so how do we go about selecting the slip angles for the inner and outer tires to construct our steering geometry.Also, how do we find the rear slip angles and hence the cornering stiffness

[JT A.]

My first question- are you talking about an actual running car, or a theoretical car that is still in the design stage? With a running car you may find it more productive to just drive the car and test different alignment and steering geometry settings. If your car is still in the design stage, these "limitations" you have aren't real limitations. You can change them.


Originally posted by Seb:
Hi,
We were facing problem in deciding the slip angles of the inner and outer tires at which we would want them to operate for extracting the maximum lateral force during cornering with the limitations we have.


Is your team a member of the TTC? If not, you should get your team to pay the $500 and become a member. You won't make it very far in the work you are trying to do without it.


With the maximum chassis roll limited to 2.4 deg (by the suspension team )

Communicate more with your team. You are the one analyzing the vehicle dynamics and predicting the car's performance. If you believe their choices are limiting the performance of the car, tell them so they can change it. You don't have to just accept whatever specs and values that suspension team (or any other team or person) imposes on you.


the Hoosier tires 20.5*7.0 which we use peaks at around 7 deg in an Fy vs SA graph
Does it always peak at 7 degrees, or does the peak slip angle change with load? Think how much load the inside tire has compared to the outside tire. This should give you an idea of how your steering geometry (inside steer angle vs outside steer angle) should be designed.



(with co-efficient of friction 0.7)
Do you mean coefficient of friction, or a scaling factor for coefficient of friction? The C.o.F. of those tires is well above 0.7


Now the problem is we are not in a position to extract the best lateral force that can be generated by (due to chassis roll limitation) our tires

Can you explain why you believe the roll limitation is limiting your lateral acceleration? I think you have some kind of misconception about how they are related. But if roll limitation really is hurting your performance, why can't you change your roll limitation? Springs and antiroll are simple to adjust.


so how do we go about selecting the slip angles for the inner and outer tires to construct our steering geometry.

I gave a hint about what to look at earlier, but here's some more detailed advice.

One quick and dirty way is to make an excel spreadsheet where you can plug in a corner radius, forward velocity, and steering angle of each wheel. Have it calculate load on each tire and slip angle at each tire (you can find the equations in various books like Race Car Vehicle Dynamics of Dynamics of the Race Car by Danny Nowlan) Slip angle equations are usually given for the bicycle model so you may have to modify them to include track width. Or if you really wanted an education exercise, you could derive them from scratch. Either way, input different speeds, corner radii, and steering angles, and plug the resulting loads and slip angles into a tire model that outputs lateral force (which will be perpindicular to the wheel, so you have to modify it by the steering angle to get force perpindicular to the chassis). Find the combination of steering angles that provides the most lateral force for each corner radius, and design your steering geometry accordingly.

A more comprehensive way is to write a program to create MMM diagrams (Milliken moment method). They will tell you much more than just peak lateral acceleration. You can find info on how to generate the plots in RCVD, and there have also been some posts on this forum and the TTC forum that give a general outline of how to do it.



Also, how do we find the rear slip angles and hence the cornering stiffness

Slip angle and cornering stiffness are only related in the linear range of the tire's slip angle vs Fy curve (+/- 1 or 2 degrees of slip angle before they start becoming nonlinear). You can find the cornering stiffness by processing the TTC data, but you won't be able to use it to calculate slip angles from track data because your drivers shouldn't be operating the tires in their linear range very often.

[Claude Rouelle]

Seb,

Just a few basic remarks....

1. You do not "decide" your slip angles. Your car, your tires, your road friction and your driver (steering, throttle, brake, gear etc...) do.

2. You need to think COMBINED lateral and longitudinal model. There will be either rolling resistance (coast down), or driving or braking torque and therefore some tire Fx. Tire friction can be represented by an ellipse. The more Fx the less Fy. And vice versa. It is an ellipse, not a square or a rectangle; you cannot be a winner on both Fy and Fx at the same time. Fx and Fy (and Mz and MX) are vertical load, slip angle, slip ratio, camber, pressure, temperature, speed, wear, heat cycles number etc.. sensitive. Make it simple first and only take the first 5 inputs into account.

3. You need basic tire model and you need to understand tire models. TTC is a good way to go. Practically the only way. You do not need TTC data to make a good car but a) it will take you more time without it b) you need it to understand WHY it is a good car. If you do not know why you win you won't know why you loose. If you do not know your strenghts you won't know your weaknesses.

4. 2.4 degrees roll is for passenger car (and even...!). Try somewhere between 0.5 top 1.0 deg roll/ lateral G. You cannot have one of your team member imposing you 2.4 degrees of roll not more than you can impose to that team member your tire slip angles. Must be a team work.

5. Be careful: are your 4527 N in the tires of the chassis coordinates?

6. Good remarks from JT A. Take them into account.

7. Who the heck are you? Didn't you have parents or educators who one taught you to introduce your self? Same remark for JT A.

[BillCobb]

And btw, since cornering stiffness is defined as the first partial derivative of lateral force vs. slip and load at a fixed load, it is a smooth continuous function throughout all possible tire usage regions. Load normalized cornering stiffness evaluated at several slip angles and two loads is usually part of any O.E.M. tire specification. Same for aligning moment. FYI FY (that's cute, eh), Since this function has sort of a bell shaped curve, some bell shaped curve traits can be used to predict the effectiveness of tire constructions on performance. You know, like a 2 or 3 sigma deal? A high peak but low sigma ain't gonna cut it so good as a wider sigma value in closed loop control. That's part of an intelligent search for the 'best tire' on a car. Just sayin'...

Also, perhaps someone was thinking of 'cornering coefficient' as a limited use metric. That's simply the load normalized lateral force taken at 1 degree slip angle. That has also been associated with O.E.M. tire specification. However, comma, since tires (and vehicles) have improved so much in the past decades) the 1 degree slip metrics are ancient history. That could be .35 g on a sporty car these days (and about at the legal limit of operation on most U.S. roads.

And Claude, I do believe the 2.5 deg/g roll spec (assuming it includes the tires) is appropriate. Most passenger cars are in the 5.5 to 7.5 deg/g roll gradient range (based on tests performed to measure such metrics). In fact, your Saab convertible is probably about 6.5 deg/g.

I believe the emphasis on getting tires to operate at the exact peak of side-force capability is a waste of time. First of all, tires operate in pairs (inside outside) and on axles (front rear). Unfortunately, the optimization also involves a displacement constraint (as in cones or guardrail) that adds a turning (yaw velocity) component to the sideslip force optimization loop. A decent simulation will show you this. Also, slip and steer angle are no longer very effective at high slip angle because the tire is a softening spring-like device and is deaf to the screams of a driver. It only 'listens' (somewhat) to camber and vertical load changes at that point. You can play with this scenario all you want with a simple (but elegant if I may say so) constant radius test Matlab simulation model I posted on the TTC forum.

I am BILLCobb, 40 years in the Vehicle Dynamics arena at GM Proving Grounds (retired). I now do custom farm work, refurbish vintage windmills, repair old school clocks and hunt with 4 black dogs in Brighton Michigan. You can find me on LinkedIn:

http://www.linkedin.com/profil...sponsive_tab_profile (http://www.linkedin.com/profile/view?id=61690164&trk=nav_responsive_tab_profile)

in the middle of a field, or out in my boat.

[Claude Rouelle]

Bill,

My Saab convertible is probably 6 deg/G but I rarely take more than 0.5 G of lateral acceleration (contrarily to 10 years ago, even worse when I was 20) Now the competition I have with myself is fuel efficiency and I am able to make over 500 miles with 1 gas tank). Still at 0.5 G lateral it would be 3 degrees of roll and I hate it. It feels like a boat. And I am not speaking of the delta front - rear roll that I can feel (and even HEAR! when I cross a railroad ) due to the like of chassis torsional stiffness (typical issue with a convertible but on that one Saab did not do a good job)

I respectfully disagree with you (and you know how I respect your knowledge and experience) about admissible range of roll gradient for a FSAE / FS. A Formula 1 is about 0.5 degree to maximum 1 degree of roll (about 1/2 on suspension and 1/2 on tires) for over 4 G of lateral acceleration. Same for an LMP1. A FS/ FSAE car is not a F1 or a Le Mans car but it is closer to it than from a passenger car. At 2.5 deg / G roll (and 1.7 G for a non aero car, 2.5 G for an aero car) the car will not be very responsive.

But if a FSAE / FS can be quick with 3 deg roll / G (on suspension, tire stiffness excluded), I will be the first one to tell I was wrong. If they do so they must have good a well thought kinematics with good toe and camber control in roll.

[Charles Kaneb]

One limit on how soft a roll rate you want to use is the amount of suspension movement required.

If your car is about 57.3" wide, then 2 degrees of roll will extend the inside-side suspension about one inch and compress the outside-side suspension about one inch. Geometric concerns can change this first approximation, of course.

What happens to your roll rate when you run out of suspension travel - topped out or bottomed out? What happens to your chassis or body ground clearance on the outside side of the car when the chassis rolls that much? If you're at 1.5 deg/g, and you pull 1.5 g, how far does the car roll?

I am Charles Kaneb and Texas A&M brought a car without any anti-roll bars to Lincoln 2013. JT A is from Kansas University.

PS: I'd like most of the passenger cars I drive to be a lot stiffer in roll, pitch, and heave. Scraping the bodywork whenever I use the brakes or bottoming out whenever an outside wheel hits a bump isn't great.

[BillCobb]

Don't forget to include the tire deflection in your roll gradient calculations. The sprung mass roll includes the unsprung mass roll contribution. As such, measurements tell the tale. If you have any sprung mass torsional compliance, its also being measured. Please don't say you don't have any (tire and chassis roll contributions). K&C tests of a few local schools FSAE cars show otherwise.

[Charles Kaneb]

(off topic) Bill, do you happen to know where an FSAE team could get a K&C test performed? Who other than the OEMs would have a K&C machine? What order of magnitude of $$$ are we talking here?

The tire deflection both laterally and longitudinally of an FSAE tire is huge. TTC gives the spring rates for these tires in the data, and our results match theirs - and they can't be neglected in even the simplest analysis. Think .25 deg/g + for the tires.

[JT A.]

Washington won some free K&C rig time for winning design at FSAE Lincoln last year. I think it was provided by Goodyear but I'm not sure.

[DougMilliken]

Washington won some free K&C rig time for winning design at FSAE Lincoln last year. I think it was provided by Goodyear but I'm not sure.
Another option is http://www.morsemeasurements.com/ located east of Charlotte, NC.

[Zac C]

Washington won some free K&C rig time for winning design at FSAE Lincoln last year. I think it was provided by Goodyear but I'm not sure.

I'm responsible for the Goodyear SPMM. Washington hasn't been able to make it onto the machine yet. The logistics just haven't worked out (machine and team are 2500 miles apart). Their test time doesn't have an expiration date attached to it though so they'll get on it sooner or later.

We aren't really setup for paid testing right now. Morse Measurement has an identical rig to us that's available for public testing. The last I checked, their test fee was something around 4-5K for a normal passenger car. FSAE stuff will probably be more expensive because of the short wheelbase. Only being able to test half the car at a time really extends the day. You also aren't typically making any configuration changes when you characterize a production car (at least I tend not to).

All the OEM's have a K&C rig though. If you can work out a sponsorship deal with Chrysler, Honda, Toyota, Ford, GM, etc. you might be able to talk your way onto a machine.

and Claude, your numbers are pretty low based on what I've tested on our SPMM. Depending on configuration, I typically see 1.3-2.4 depending on configuration. This includes overall competition winners from 07, 08, 10, 11, and 99 and a bunch of cars that won autocross or finished in the top 5.

[Claude Rouelle]

The advantage of Morse Measurements is that they can do all 4 wheels and heave, roll, pitch and steering separately or combined at the same time. At least they can do longitudinal forces, pitch center location, toe and camber and wheel movements under tire Fx forces etc... which not all K&C benches can do.
Several FSAE teams already went on that test bench and learned that the results could be quite different that what their kinematics software of Catia or Solidworks told them. I cannot speak for Morse but as for anything prices are negotiable and they should give a big discount for FSAE teams, knowing that a small percentage of the students who visit their company will make Morse Measurements advertising with future OEM, tire company or race team future employers.

Zac,

I believe you. But we are not speaking about the same thing. If you target 0.5 to 1.0 deg / G in your suspension roll stiffness but then you take into account the tire deflection and the big amount of compliance you usually see in FSAE / FS cars (chassis and suspension elements) you will effectively arrive at 1.5 to 2.5 deg / G (on the K&C and probably even more on the track)

.....which I still consider way too big unless unless you have a very unskilled, non feeling, non reactive driver.

These FSAE tires are already so "lazy", that I don't see why I would want to add another soft spring in series with the tires.

It is not because the 99, 07, 08, 10, 11 winners were in the 2.0 deg / G zone that zone is necessarily the "sweet spot". It is a good indication but not necessarily the ideal.

As a general observation not specifically looking at tire or K&C data, the winner of one competition shows the best car design + setup + reliability and tires... combined with that driver that day on that circuit at that environmental conditions ... COMPARED to the other combinations. But that doesn't mean that that winning car was the best it could be. Put a professional driver in it, after a while he will make it much quicker, ask setup changes and make it even quicker.

[Zac C]

Morse measurements shouldn't be able to do a full characterization of both axles at the same time on most FSAE cars. The wheelbase is too short even if you remove the table extenders. At least that's been my experience with near identical hardware (key difference: ours is yellow, not blue). I'm also not convinced that running a pitch test is necessary.

I'm not saying that 2 deg/g is "optimal" just that the "good" cars do test in that range. I should also point out that my 2 deg/g measurement doesn't include all of the tire deflection (or the heaps of suspension compliance present). But I've seen enough cars with jacked up alignments running fast times at competition to know that these cars usually have much bigger issues than whatever roll stiffness the team has decided to run.

Also a minor point, at least two of the cars I mentioned were set up by professional drivers, one of whom would not react favorably to being called "very unskilled, non feeling, or non reactive."

[Claude Rouelle]

Zac C,

"The wheelbase is too short...."? Rotate the car 90 degrees.

"I'm also not convinced that running a pitch test is necessary" Try again. Most of the time the longitudinal camber, wheelbase and, worse toe, compliance is the biggest compliance that students (and some passenger cars engineers) usually miss. Unknown and/or unmeasured toe variation in braking and acceleration will have much more disastrous consequence on control and stability then known camber variation under steering moment and lateral forces efforts effects on camber will have on grip and balance.

The best roll stiffness is the one which makes you car fast and your driver happy. If 3 or even 5 degrees of roll is the best solution so be it ... providing it comes with an explanation that on a race car 3 degree of roll is better than 1 degree. If the explanation is logic and the arguments come with good numbers I will buy it. At this stage my experience with simulation and on track testing makes me just a bit skeptical. But I have been wrong in the past I will be again so I am open if solid arguments are presented (but in that case the transient aspects, not only the steady state ones, has to be considered)

Juts a hint I have seen several FSAE / FS cars soft in roll because that is the only way they students could cope with a harsh ride. Patch on a patch?

Another hint: most K&C a) do not replicate the real tire force (simply because the tires are too cold) and b) not take, the pitch, roll and heave damping into account.

(I should say here that most students know their ride frequency and damping but only a few of them know their roll and pitch frequency and damping ratio and this may explain that)

As for any in-lab test and/or software simulation it has its strengths and weakness.

But if a team has the chance to go in a K&C test bench, they should not hesitate, whatever test bench it is; it will open their mind and they will learn a lot.

[BillCobb]

Aren't they Anthony Best equipment ? As such I believe they can't/don't do aligning moment compliances. (yes I could be relying on older information).

But, without aligning moment inputs, a K&C test is just a software validation exercise instead of a serious way to quantify on-road handling and ride simulations.

The machines at GM Facilities (Michigan, Korea, China and Germany are all MTS jobs. All it takes to get a freeby is a connected alumni and a team with car(s) on site on a Saturday. UofM probably has a full time travel trailer parked outside of Building 7 by now.

A great use of these machines (4 wheel MTS) is the ability to 'simulate' an "inertia relief" process. You apply all the tire forces and moments at the contact patches and roll or pitch angles and then get the compliance derivatives. This may take several iterations because the tire inputs come from simulations which make use of the compliance derivatives you are trying to determine. The process (called bootstrapping) can be pretty eye opening just to see all the bending, movement and crappola present in a chassis and steering system. The car has to be mounted in a special way, too. Otherwise the clamping system artificially constrains the spaghetti tubes, beams, rails and unobtainium used in these cars.

A 'bad' set of wheel bearings on an awesome car makes for a bad car no matter how sophisticated or careful the designers of constructors are. The lurches in the data are generally not in the suspension designers vocabulary.

Without aligning torque steer and camber compliance measurements, the quantification of cornering compliances for obtaining a workable handling is a sadly missed opportunity.

(Congrats on getting the new forum underway, BTW. I was banned for life at first login...

[Zac C]

If you rotate the car 90 deg, the track width is still too short to test all 4 corners at once. You also won't be able to, you know, hook up your wheel sensors. The minimum wheelbase for a 4 position test on a SPMM (MTS will be be different) is just under 2m. Minimum track width is around 1100mm

Pitch tests aren't usually run as part of a vehicle characterization. At least they haven't been in the data sets I've received from at least 4 separate OEM's. But I guess you must know something I and presumably they don't.

Bill, Anthony Best machines can apply aligning torque at the contact patch. What you're probably thinking of is the wheel position measurement system. I haven't seen how MTS does their measurements, but AB uses string encoders. On the early machines (Goodyear and MIRA if they haven't updated it), they used a 5 encoder system that doesn't measure caster/spin. Later machines use a 6 encoder system that remedies this. The 'dynamic' SPMM's take this a step further by dumping the strings altogether and attaching something similar to a FARO arm directly to the wheel.

The big advantage of the AB machine over what MTS users have told me is the use of electric actuators vs hydraulics. But that's second hand info. The number of engineers that have worked with both machines is likely a very small group.

[Moop]

A great use of these machines (4 wheel MTS) is the ability to 'simulate' an "inertia relief" process. You apply all the tire forces and moments at the contact patches and roll or pitch angles and then get the compliance derivatives. This may take several iterations because the tire inputs come from simulations which make use of the compliance derivatives you are trying to determine. The process (called bootstrapping) can be pretty eye opening just to see all the bending, movement and crappola present in a chassis and steering system. The car has to be mounted in a special way, too. Otherwise the clamping system artificially constrains the spaghetti tubes, beams, rails and unobtainium used in these cars.
Out of curiosity, how is the car actually restrained for inertia relief? Looking through some of the files available on the web MTS mentions an optional "CG restraint" but don't give too much detail about it.

I would think that just a clamp located at the CG would be at least a little bit wrong, seeing as the force is actually trying to get to all the mass in the driver, engine etc to push it around and this would change the load path a little bit, although the difference might not be huge. It's obviously better than just clamping the chassis down wherever you feel like though.

[DougMilliken]

Aren't they Anthony Best equipment ? As such I believe they can't/don't do aligning moment compliances. (yes I could be relying on older information).

As Zac C writes, the Anthony Best Dynamics (ABD) SPMM has rotary actuators built into each wheel pad. Measurements of "aligning torque steer" and "aligning torque camber" are routine.

Bill, you might be thinking about the K&C rig designed (in part) by John Ellis? There was one of these at Goodyear/Akron about 20 years ago, it was replaced by their current SPMM. At least one version of the Ellis machine (have forgotten the full name) did not have dedicated actuators for aligning moment, but it was able to apply lateral forces at different longitudinal locations relative to the geometric center of the tire contact patch. This "simulation of pneumatic trail" was a clever way to save the cost of four rotary actuators, but, mixing Fy and Mz gave some obvious limitations in test design and productivity. There were other problems with the Ellis rig too, my memory is that it was not very reliable.


A great use of these machines (4 wheel MTS) is the ability to 'simulate' an "inertia relief" process. ...

Morse Measurements run a test like this on their ABD SPMM and have test control software to support it. I think they call it something like "track simulation" but I might have the wrong name.

Morse have also developed special wheel pads that greatly increase the amount of static tire grip. Realistic levels of Fx, Fy and Mz can be applied through a cold race tire without slipping/creeping.

[Disclaimer -- I'm a rep for ABD SPMM test equipment.]