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/Pap...cles/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/Pap...ance/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.

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?