Simulate what you can test and test what you can simulate

[BillCobb]

To reinforce the notion of using simulation pre-construction, I stumbled into this paper from a few years back and though some members might want to take a stab at doing some get-real simulation engineering with more than the usual amount of chassis detail. "You mean the tires are not the only compliant parts in a car ? OMG"

A good project for a novice Excel or Matlab wannabe. Add a bit more complexity and some TTC tire data facts with a better tire model and you might just be ready to build a car good right off the trailer and ready to test.

https://cecas.clemson.edu/ayalew/Papers/Vehicle%20Systems%20Dynamics%20and%20Control/Papers/An%20Iterative%20Approach%20for%20Steady%20State%2 0Handling%20Analysis%20of%20Vehicles/641_1.pdf

[rory.gover]

Bill, I thought you might enjoy the below paper as well. Would be relatively easy to get tyre relaxation data from TTC, get Fy and Mz compliance effects in (that data is harder to come by for FSAE teams as it's not on the internet) and do a chirp steer test. Compare the TFs with what you may measure experimentally.

Okay then, what does a "good" TF look like for yaw, normal accel gains and understeer.

https://cecas.clemson.edu/ayalew/Papers/Vehicle%20Systems%20Dynamics%20and%20Control/Papers/On%20the%20Frequency%20Domain%20Analysis%20of%20Ti re%20Relaxation%20Effects%20on%20Transient%20On-Center%20Vehicle%20Handling%20Performance/755_1.pdf

[BillCobb]

Thank you for that reference. I'll bite offand chew a few comments:

1) There is relaxation data available on the TTC, AND an example of it processed posted by me, including it's use in simulations where speed adjustments are made.

2) The only real compliances applicable to a FSAE car are probably steer and camber related, more so front effects (front steering).

3) The TTC relaxation tests are representative of the steered (By a steering mechanism). This is the Control Input. The unsteered tires (as is likely rears) don't have the same responses as they are plunged into a turn because of the vehicle's yaw and sideslip response and not steered by the driver.

4) Note that the steered tires Mz response is the most interesting because of it's effect on compliance AND on the rigid body yawrate transient. A feeling driver ought to e able to sense this torque in the steering wheel if the steering mechanism is good and the drivers hands and fingers aren't welded to the rim.

5) Experimental methods CAN be used to ascertain transient tire characteristics in the long range view. Given a chirp or square wave pulsed
steer input to the car AND a Cornering Compliance based set of transfer functions (Cornering Compliances as in there's more than just some
tire compliance in the vehicle), a Optimizer can be coaxed into producing the cornering compliances that mimic the road test results
(Yaw Velocity and Sideslip gains and steering sensitivity (Ay by SWA). However, if you don't include a tire relaxation term, the solution
will not converge. This is because there will be a phase error that can not be closed. An extra velocity term is necessary for both gain and phase
characteristics to be matched. This will be the lumped tire relaxation effect.

6) Understeer is a derivative, not a difference variable. I have seen more than one 'vehicle dynamicist' use difference metrics and then get bamboozled by the appearance of real road test results which are not increasing or decreasing functions, but curl back on themselves. This would really mean a severely oversteering vehicle yet it would be published as an understeering condition.
Limited slip differentials come to mind as players in this nomenclature game.

I can post a few transfer function views of what the bob & wow FSAE cars might be (best of the best and worst of the worst) if anybody is interested.

[rory.gover]

I am aware of a number of teams looking into the relaxation data based on your TTC posts. How far they are towards instituting it into a viable simulation and specification tool, I am unsure.

Hadn't thought much about the rear transient development too much, to be honest. Will need to give that some cycles in my thought process at some stage. Agreed, that their definition of US is not particularly satisfactory.

I know there is at least one soul interested in your BOB and WOW approximations are for FSAE vehicles.

[turtle]

I assume, if I had good confidence in my design-time parameters, the difference between the steady-state simulation and the test result (if I had any) could be attributed to some sort of compliance. How would I pick my understeer target in the first place?

[BillCobb]

I assume, if I had good confidence in my design-time parameters, the difference between the steady-state simulation and the test result (if I had any) could be attributed to some sort of compliance. How would I pick my understeer target in the first place?

That's a very good question. Since FSAE cars don't run at break-neck speeds, one of the two principle advantages of an understeering car is the attenuation of steering gain with increasing speed. (it's speed squared actually). So, you would want to know what the min and max speeds you would be maneuvering with so the drivers ability to control the car with a 'comfortable' steering wheel angle range is established.
Obviously the steering mechanism ratio factors into this, with an additional constraint of the max tolerable steering wheel rim force. BTW, my own sims of this type of car indicate that just weight/tires, speed, and wheelbase show them to be kinda lazy, (High cornering level/ability, but disappointing transient responses, even with 50/50 weight distribution.

The second contribution of understeer is to increase the car's natural frequencies. Thus they become more responsive. You would want the response times / bandwidth to be within the driver's own range of perception so that they don't have to wait for a response to develop and thus be tempted to anticipate a sluggish vehicle.

Since the tires on these cars are so large compared to their design static and dynamic axle loads, getting even a neutral steer car is difficult to obtain unless you do it the smart way instead of the easy way. And, it's not likely that the open loop oversteering car is unmanageable, you just have to control it all the time. Understeer costs you max lateral capability because you don't get to use the max force of both axles.

If I were running a team, I would build a car, validate it with simple measurements, (constant radius and frequency response tests), then run a matrix of tire properties (size and pressure) and weight distribution and ask several drivers to evaluate the conditions. One who can tell the difference between all conditions is still in the running. The rest wash out,
Then run lap times on a course which challenges the car and the driver. The correlation is pretty much established as to what your steering and steering torque gains are as well as the response times you can afford.

The learnings from this are tremendous. That's why you build simple, test as often as possible and train your driver(s). Then you will have good cars on the hauler when you ship them and can enjoy the scenery at the track instead of the taste of grease, skinned knuckles and cold hot dogs.

[turtle]

I guess it comes down picking the combination of front and rear cornering compliances I can afford to have then.

Speaking of simple measurements - if I had nothing in terms of instrumentation, what would be the single most valuable test I could do with parts off the shelf? EDIT: Bonus - and what would be the simplest simulation I could use to correlate/validate/study the test results with?

Curious what an unstable driver could do with an unstable car, assuming it would create a closed-loop stable system.

[BillCobb]

There are two simple tests ALWAYS run on mule or prototype cars headed for road tests:

1) a 'Ride Toe' test. Do it on a wheel alignment machine if possible. Otherwise, measure each wheel on an axle as you raise and lower the car to
max and min jounce and rebound positions. Use sand bags and a floor jack if you have nothing else. Toe change readings ought to be the same left and right. and the slope ought to agree with your linkage analysis predictions. If not, its misbuilt.
You need some sort of accurate steer and height measurement gear. Heck, glue some pocket laser pointers on the wheels and project to a wall (after calibration of some sort). Same with height. These measurements won't be the same as "roll Steer" values because you are loading the tierods opposed instead of that in a lateral/roll maneuver. This also tells you that your ride height is correct and that your steering gear is level and not cock-eyed in several directions.

2) an Overall Steering ratio test. Measure both steered wheel angles and the steering wheel angle using small steering wheel angular inputs. Place the wheels on grease plates or air bearings or wheel alignment pads. You don't want the tires to scrub at all. The crossplot will show symmetry, Ackermann error and proper Cardan joint phasing (if one or more joints are used)

If the results of either of these two tests is crap, the car doesn't leave the garage until the results look good and compare to design intent. A road test with lousing steering and crummy geometry won't fix incorrect construction, compliance, loose parts, bound up parts, or improper position(s).

Once these two indoor lab tests are good to go, get something together that can measure and record yaw velocity and forward speed. Run a fixed steering wheel test in a parking lot somewhere at several initial steer angles. Hand held is NFG. Clamp the steering wheel.
Cross-plot Speed x yaw rate (lateral g) vs yawrate over speed (curvature) (get the units right) and compute the slope. You will need to know the wheelbase for this calculation. The slope of each line you generate is the understeer/oversteer of your car. I believe I posted this procedure and some Matlab processing code on the forum some time ago.

Don't be surprised if your little race car is understeering when you have data. Some pretty sloppy steering systems can outweigh the oversteering weight and tire contributions coupled with a limited slip or solid drive axle.

A good driver can easily operate an oversteering vehicle to some extent but will complain about the transient response (its very sluggish). It depends on the amount of oversteer. An oversteer car is not necessarily unstable. The gain will increase at a high rate with increasing speed to a point where just breathing on the wheel will make it undriveable (twitchy). These cars can be inherently oversteering because of the weight distribution and the use of the same tires on front and rear axle (hint: try something other than this). And, they don't really go that fast. Give me a call when someone wants to try driving one at 160 kph though. Its gonna be a "here, hold my beer" moment.

[DougMilliken]

There are two simple tests ALWAYS run on mule or prototype cars headed for road tests:

Bill -- great summary! If anyone is interested in a more detailed discussion with some sample plots, see RCVD Chapter 19 on Steering Systems.


Once these two indoor lab tests are good to go, get something together that can measure and record yaw velocity and forward speed. Run a fixed steering wheel test in a parking lot somewhere at several initial steer angles.

When we wrote RCVD, instrumentation (including yaw rate sensing) was often expensive, so we suggested using the constant radius, variable speed test, using lap time around the circle as a primary measurement of Ay. Similar results to the fixed steering wheel test. Pop quiz: describe the differences between these two tests, can you convert results from constant speed testing to constant radius testing? Discussed in more detail and with plots in Section 11.7, starting on page 383.

[turtle]

Since FSAE cars don't run at break-neck speeds, one of the two principle advantages of an understeering car is the attenuation of steering gain with increasing speed. (it's speed squared actually)

I need to convince myself of a few things. Lets plot the lateral acceleration steering gain of an understeering, oversteering and neutral steer bicycle with respect to speed.
http://i.imgur.com/Ku5lWvj.png


BTW, my own sims of this type of car indicate that just weight/tires, speed, and wheelbase show them to be kinda lazy, (High cornering level/ability, but disappointing transient responses, even with 50/50 weight distribution.

By lazy, do you mean that the response looks almost first order?


A good driver can easily operate an oversteering vehicle to some extent but will complain about the transient response (its very sluggish). It depends on the amount of oversteer. An oversteer car is not necessarily unstable.

Hmm that's interesting. I've convinced myself that at oversteer does not necessarily mean open-loop unstable. However, there is a point where if I increase my rear cornering compliance too much, the step response blows up. The response of my oversteering example is definitely sluggish and appears to be dominated by the exponential response (no overshoot), but I would have thought the transition between the open-loop stable oversteer and open-loop unstable oversteer to be a little bit more exciting. Is there any significance to this transition?

[DougMilliken]

You might take a look through SAE 205A "Motions of Skidding Automobiles", Radt & Milliken. 1960. If you can't get the paper from your library or SAE, let me know.

[MCoach]

If you don't have any data acquisition at all....do not dispair! You still have some tricks at hand that you can use.

If you run skid pad at several radii increments you can use the vehicle time to complete the each cycle, which allows you to calculate estimated lateral acceleration.
While running these tests, if you place an O-ring on your damper shaft and push it up to the face of your body, you can that to find your max damper travel during each event.
(as pictured in attachment, Doug may remember me suggesting this during the MIS design review last year :) )Combining this with the shop/lab tests suggested by Bill, you can tell a lot about your car.
You can do the same with your steering rack. This will allow you to find max steer travel during the event. Again, combining this with lab kinematic measures can yield useful data.

You can go on to do this for transient events such as slaloms as well. But, I suggest you start small, go fast, and turn left.

I suggest you take those lab measurements, and turn them into suspension travel fit equations, then with a laptop and a set of calipers to measure the O-ring distance from the shock body you can figure out almost exactly how much steer angle you are using, your camber used during these events, the ride height of the car all around, pitch, roll, etc.
If you have some way to record suspension movement, these can be turned into math channels instead, and recorded on your logger.

Word of warning: These kinematic measurements neglect the compliance occurring unless you have an estimate for that from Bill's lab measures as well.


If you do have data acquisition, preferably an IMU (3 axis accel, 3 axis gyro) or even just lateral accel and yaw rate sensor, I would suggest the increasing radius, slaloms of various spacing, and a "tire scrubbing" maneuver.
Tire scrubbing, as in driving at slow speed in a straight line and sawing the wheel back and forth from limit to limit.
This might not be an intuitive test, but the tire scrubbing maneuver can show you your "torque reserve" (analogous to engine controls) as I've started to think of it lately.
This is essentially how much total aligning torque (Mz) your car is able to produce at that particular speed that is not being used up by the tire to produce lateral acceleration or longitudinal acceleration, which can be important for the short, technical sections of the track.

[BillCobb]

"at the roadwheel" is a common oversimplification and may be the reason so many cars are mischaracterised and so many simulations come out wrong.
You may be missing the compliance (or lack of) at the tierods (buckling), at the rack (mounts and rack/[imion pushaway) and the intermediate shaft (Cardan joint out of plane moments),
Last I saw, a driver uses the steering wheel to drive and all measurements are universally referenced to it.

By "lazy", I mean slow, takes a relatively long time to evolve. Usually slower than the preferred perception tim of an experienced driver ( < .28 seconds or better). Unsersteer doesn't reduce damping, it raises the plant's natural frequency. Look a where (DF -DR) appears in the transfer function denominators.

The oversteering vehicle is stable at a specific speed until the the amount of oversteer exceeds the so-called Ackermann Gradient. Then the denominator goes negative and all your state variables go south (or north depending which hemisphere you are in. The Ackermann Gradient components tell you that a longer wheelbase is good, a lower speed is good, and I suppose smaller values of PI would help.

Since the Ackermann gradient goes down squared with speed, there's not a long of help from it when you are going REALLY fast.

[Billzilla]

While running these tests, if you place an O-ring on your damper shaft and push it up to the face of your body

A cable-tie works just as well and it much easier to fit & remove.

[BillCobb]

I need to convince myself of a few things. Lets plot the lateral acceleration steering gain of an understeering, oversteering and neutral steer bicycle with respect to speed.
http://i.imgur.com/Ku5lWvj.png



By lazy, do you mean that the response looks almost first order?



Hmm that's interesting. I've convinced myself that at oversteer does not necessarily mean open-loop unstable. However, there is a point where if I increase my rear cornering compliance too much, the step response blows up. The response of my oversteering example is definitely sluggish and appears to be dominated by the exponential response (no overshoot), but I would have thought the transition between the open-loop stable oversteer and open-loop unstable oversteer to be a little bit more exciting. Is there any significance to this transition?

Take a look at what is probably more like a FSAE car:

DF=2, DR=1

and
DF=2, DR=2

and DF=1, DR=2.

Total wgt = 200 kg, distributions 40/60 and 50/50, wheelbase = 1600 mm, steering ratio 4:1, Max speed 100 kph.

These factors are likely good up to 1.0 g or so, then you gotta take charge.

[BillCobb]

I assume, if I had good confidence in my design-time parameters, the difference between the steady-state simulation and the test result (if I had any) could be attributed to some sort of compliance. How would I pick my understeer target in the first place?

You would not pick the understeer as a target for a FSAE car. That would be a constraint, goal or target if you were designing a vehicle with large payload changes or anticipating forseeable misuse by owners replacing tires with aftermarket skins, etc.
In this case, you would want to pick front and rear cornering compliances to deliver an optimum transient response suitable, acceptable and comfortable to your driver. That means you would choose the system dynamics of your car to work within their skills, reflexes and reactions.

Here is a simple textbook kind of example of the technique.

Lets say you have some sort of foundation of your car's architecture: Total weight, weight distribution, and speed range to be encountered.

Plop them into a synthesis tool which can map out transient responses from hypothetical top tier chassis + tire subsystem specs:
1164

Run a play which produces an array of response time vs. front and rear cornering compliance. Lateral acceleration response time is clearly the specific trait correlated to pleaseability. A crude display of this is also shown.
1165

Now you need the response time target for your driver and a list of possibilities for one end of the car as far as the tires and K&C recipe:

Based on cost, availability, performance and tuneability, let's say your team could produce a front cornering compliance (DF) of 3.00 deg/g. Then your requirement for a rear cornering compliance (DR) would be 2.47 deg/g on a 0.30 sec response time requirement, leaving you with an underteer of 0.53 deg/g.

If your front tires and chassis can produce a DF of 2.00 deg/g (more likely), then your DR could be 2.017 deg/g and a slightly oversteering car. Does this all start to sink in ?
This changes a bit if your driver has better reactions (let's say .24 response time more likely for Fangio) then your DF of 2.00 deg/g would need a DR of 1.79 deg/g to queue with such a driver.

Keep in mind there are a few other issues here but the process is the same. Here I chose DF as a starting reference. Most of the time it would be DR, but you get the picture. And there is consideration for what happens as your g levels rise. FSAE car tires are so large, that their properties really don't change that much
over the range of useage as I see. Wild guesses as to great nonlinearity are from wild imaginations. That's why the TTC is necessary.

The next drill down would be to evaluate all the tire data to find tire properties that can deliver your DF when you add some sort of steering system. That's not always easy because of tire availability, steering mechanism limitations and packaging, etc. Finally, given the gain of the car in the speed range you are working with, you choose a steering ratio that minimizes hand movement and broken arms and shoulders from excessive steering torque. (did someone mention power steering for low speed maneuverability ???)

Let me also remind you that as you reduce the steer ratio, reactions loads go up big time, so steering compliances get jacked up. It's very possible (and common) for a 'quicker' gear to produce a 'slower' car because the increased compliance slows the car's gain down faster than the quicker gear speeds it up. Sheet Happens !

[turtle]

It seems to be a ghost town here, but there is a lot of useful information to digest. I will just go right ahead and ask more questions even if I don't fully understand everything just yet. Maybe some homework is in order ;)



You might take a look through SAE 205A "Motions of Skidding Automobiles", Radt & Milliken. 1960. If you can't get the paper from your library or SAE, let me know.


Looks like the library archive goes to 1967 on microfiche (!!). The paper preview starts with a presentation of the model though I would be interested in what is presented after the model.



While running these tests, if you place an O-ring on your damper shaft and push it up to the face of your body, you can that to find your max damper travel during each event.


This is a very clever trick that I've got to try now.


You would not pick the understeer as a target for a FSAE car. That would be a constraint, goal or target if you were designing a vehicle with large payload changes or anticipating forseeable misuse by owners replacing tires with aftermarket skins, etc.
In this case, you would want to pick front and rear cornering compliances to deliver an optimum transient response suitable, acceptable and comfortable to your driver. That means you would choose the system dynamics of your car to work within their skills, reflexes and reactions.


Wow! Lots of information to break down here. I understand the motivation of trying to design an FSAE for 'optimum' transient response. What I do not understand is how you design for variation in your vehicle model like in the road vehicle case you mentioned. Is there any reason to consider something like payload variation (heavier driver??) for an FSAE? And if so, how do you 'design' for these variations?

Returning to the theme of simulation/testing, let's go back to the scenario of being broke without a fancy data acquisition system. Synthesis is one part of the puzzle, but what about characterization? Is there a simple way to invert this process from some sort or road test information to derive how far off the car was from it's design targets? I know it's discussed a bit in the other threads you have but I might as well bring it up.

Another piece of the puzzle is finding the right driver. As much as I would like to think that I am a karting champion, the reality is that many of us are not the greatest driver. How can the transient response specs be selected early in the process such that the vehicle design accommodates the wide range of amateur drivers that I have to work with?

[BillCobb]

It's a ghost town because so few members know what 'simulation' actually is. They confuse simulation with 'tools' . In that case, my best simulations here on the Farm are my Milwaukee battery impact driver and a 1/2" (13mm) box wrench. The catch all is a pair (2) of vice grips and a large flat head screw driver for mounting tires and fixing flats. These are my highly correlated simulations. I get good lap times around the fields with good tires.

In fact, this FORUM is a TOOL, thus, I'd guess its a simulation !

Meanwhile, 'Design Variation' usually involves 'Build Variation' because of all the slotted holes teams think they need. Instead, a well done suspension parameter modeling TOOL which include not only geometry but compliant bodies is used to produce a variation analysis. You fire thousands of random misbuilds at the 'tool' (Monte Carlo Analysis) and recover the SDF's (Suspension Design Factors). That include ride/Roll steer, compliance steer and camber, roll centers (force method), asymmetries, etc.
This is then analyzed in bulk to identify the points and member elements with the highest participation is misbuild conditions. THOSE condition get the most emphasis during construction and part selection. You ought then to be able to 'net build'. You don't need all those drill holes that show only that you have no idea what you are doing, just wandering around, lost in the uncertainty forest. That's Monte Python Analysis. An alternative to the Monte Carlo technique is the BOB and WOW process. Best of the Best and Worst of the Worst. Build boxes around values for your key design parameters and evaluate your System Model with the 4 values in each position.

For testing, search elsewhere in the forum for a "Characteristic Speed Test" procedure I submitted. Knowledgeable readers may recall that I measured the understeer of my speed boat. It's understeering with a 3 blade propeller, neutral with a 4 blade and oversteering with a 5 bladed Mercury Hi-Five ported prop.

The right driver ? Eliminate the wrong driver(s). Its a show-me contest usually involving several cars: good, bad and ugly. A good driver produces the best times, saves the car parts (and tires), is smooth (smoove), and can tell you why. SCCA Autocross might be a good starting qualification, good technical background, a good balance of left and right brain functions (need the haptic elements). has had early childhood exposure to more than 0.1 g lateral force, and has not had severe head injuries from crashing their hot air balloon.

That is all.

[turtle]

From Merriam-Webster

Tool: a handheld device that aids in accomplishing a task
Simulation: the imitative representation of the functioning of one system or process by means of the functioning of another

Tools with bad simulations. Simulations with bad tools. Maybe the definition of usefulness is when you have both!

Couldn't find the characteristic speed test procedure, but I did find some references to it on another forum dating 2007.



Vbox or equivalent process for fixed steer understeer test:
Measure speed and yawrate or speed and lateral acceleration while SLOWLY increasing speed. Be careful about shifting gears so pick them wisely. Do this for several radii. Then from ay compute yawrate. A Vbox actually only measures steady state g so its perfect. Then in Excel or Matlab or whatever, make up a function with lateral acceleration on x axis and curvature (yawrate/speed) on y axis. Compute the slope of these multi-radii functions in both directions. The understeer is the negative slope of this function times the wheelbase in radius units. There is a pi thing in there, 2.


If only I could extract DF/DR from a test as simple as the fixed steer understeer test

[BillCobb]

Several recent papers out there showing use of raw data from an Android phone (GPS, gyro, and ay) to calculate vehicle dynamics test values. Some may snicker because they can afford to use a $20,00 sensor, but what have you got to lose ?

All you need is sisu.