Modeling hysteretic elements when specifying dampers 4

[hutch325]

Okay, time for a long post.

I am looking for advice on simulating some suspension elements. I currently have a quarter-car model in Simulink (MATLAB) that I am using as a tool to specify damper characteristics for a BMW using stiffer springs than stock (along with some Excel-based calcs for natural freq. and damping ratio).

A little history: I got started on this after being unsatisfied with the various aftermarket suspensions available in kit form and essentially ended up increasing the spring rates significantly and using some "sport" dampers at least for a trial run (that was a couple years ago). I've gone through a few different setups with various levels of analysis before testing each one. I wish I could say it has been a well-designed test program but realistically it has been a learning experience done in the evenings after my day engineering job (much to the chagrin of my fiance in some cases).

In any event, I am running into a couple roadblocks. My model includes tire stiffness, spring stiffness, damper characteristic (non-linearity modeled using a lookup table), and accounts for the motion ratios of the spring and damper. Two things I am looking for suggestions on:

1. The tire vertical stiffness model.

Originally I was not modeling the tire stiffness as I am not really concerned about the wheel hop mode for now, but later I added a tire stiffness after encountering some odd bouncing after hitting certain bumps, particularly with the rear suspension. It turns out the rebound damping was too high, and the suspension was extending quite slowly while the tire sidewall oscillated, resulting in some interesting harmonic motion. The characteristic was not exhibited on the racetrack since the surface is quite smooth but on the street (especially in Pittsburgh) it was quite noticeable and certainly unacceptable.

After adding a simple linear spring to model the tire, I am able to at least produce a prediction similar to the actual results, but I am looking to refine the model. As an initial guess I am using a stiffness 1000 lb/in (for a 225/50-16 tire). Any suggestions on an appropriate stiffness value to use? Or an appropriate damping ratio or hysteresis to model? Or an SAE paper or reference to search in? Milliken's RCVD doesn't seem to provide any info on this particular tire characteristic (at least not that I've found).

2. How to model the elastomer springs

I currently have no model for the elastomer springs, mainly because I don't know how I should model the hysteretic characteristic (i.e. I don't know what the characteristics are - making the model once I have an idea of the characteristic shouldn't be a problem). Will the elastomer spring rebound fast enough that I will need to account for its stiffness when specifying the damper characteristic, or does it essentially function as a progressive rate spring in compression and then have a zero rate in rebound? I suspect neither modeling it as a pure spring nor only considering its stiffness in compression is the correct strategy. Unfortunately, testing is pretty much out of the question. Again, any suggestions or suggested references? I did find one that has potential on the SAE website:

http://www.sae.org/servlets/productDetail?PROD_TYP=PAPER&PROD_CD=910109

Does anyone know if it contains useful information?

I do realize I'm just touching the tip of the iceberg with the quarter-car model but I don't have access to more advanced software such as ADAMS (although I am using Susprog3D for geometry calcs). Testing is pretty much limited to spring/elastomer static stiffness, damper characteristic measurement, and road and track testing.

Thanks for any information, and critiques are welcome.

Chris

 

[GregLocock]

1)A bit low 200-250 N/mm is more typical.

If you want to learn more about this, try dropping your spare wheel on a concrete floor. You should be able to estimate the damping and the stiffness from appropriate observations.

2) which elastomer springs - the spring aids? we treat them as springs. Their damping contribution will be very small.





Cheers

Greg Locock

 

[hutch325]

Thanks for the reply, Greg.

Interesting and good suggestion regarding dropping the tire. Thanks for the ballpark stiffness value. Is there a refrence in the public domain containing information like that so I can consider other tires without having to test each one (like if I want to consider a tire I don't have)?

Regarding the elastomer springs, I suppose spring aids would be the proper description. A foam spring installed on the shock absorber. I've heard them called elastomer springs, bumpstops, and "microcellular jounce dampers". It's easy enough to for me to treat them as springs so I guess that's what I'll do.

On the more practical side of things, is it typical to include tire stiffness and elastomer springs when specifying damping with respect to the sprung mass, or am I going off into left field?

 

[MoreWing]

Leave the bump rubber (spring aid, foam spring, etc.) out of the damping equation. You only want the suspension on the bump rubber when you are to the point of bottoming the suspension. Having said this, you'll be suprized how much you can use a bump rubber and not have it upset the handling. If coupled with a reasonable spring package, using bump rubbers will actually give you the opportunity for a better ride. What type of bump rubber are you using? Penske Racing Shocks has a series of bump rubbers that are probably pretty close to what I would run on a road car app. If you're curious, I could dig up my testing on them and give you an idea on the various spring rates.

The damping in a bump rubber is pretty small. I've ran them on a shock dyno and the hysterisis is visible, but small.

For curiousities' sake, what kind of damping ratios have you tested and what are the trends that you are finding? It sounds like you have already found the upper limit of rear rebound. What kind of dampers are you using?

Cheers

 

[GregLocock]

We use constant contact polyurethane foam spring aids, mounted on the shock. These give a rising rate spring. In our case they first come into play at about 10mm below design ride height, that is, at design, they are already compressed by 10mm. Big gotcha - they are very non linear.

I don't know of any useful source of tyre data, we test everything.

I don't know if people generally use the tyre stiffness in their models for shock settings. I would. My shock model is pretty crude, so/and/because I don't do shock tuning in the models.

Cheers

Greg Locock

 

[MoreWing]

Constant contact, huh. I have tried that, but never really got the results I was looking for. It seemed that the bump rubber I was using was a little temperature sensive or something. It just didn't work for any long period of time.

I use soft(ish) springs for good mechanical grip (read "ride"). I'm not shy about running in the bump rubbers through some corners as long as the car constantly has the bump rubber engaged, but out of the non-linear spring portion of travel. In that scenario, it's just another spring, and the stiffer 'spring' is better for high speed stability.

The last thing I use them for is to keep the car from bottoming, generally high speed braking is the biggest culprit here. The rising rate that you end up with allows you to put a stop to suspension travel very quickly right before the bad stuff happens. Generally speaking, I think that bump rubbers are quite under-appreciated tools.

I've found as much as a 10mm ride height difference between using bump rubbers and not using bump rubbers. That's a significant difference.

 

[hutch325]

The bump rubbers are what were supplied with the dampers, which are Bilstein (monotube design).

At stock ride height, and using the BMW bumpstops, for the suspension has to be compressed about 0.75-1.0 inch before the bumpstop is contacted. So yes, you are correct that it would take a big bump for them to come into play. I figure I can measure the stiffness of the bumpstops easily then incorporate them into the model, with an appropriate deadband to represent the suspension travel prior to contacting the bumpstops. That way I can examine the response if I were to hit a huge bump, but use damping ratios as my basis for my initial damper characteristic design.

MoreWing - I would definitely appreciate seeing your test data on the Penske bump rubbers, if you still have it available.

With respect to damping ratios, I have really only been looking at rebound damping so far as I think I don't want much overshoot of the sprung mass, which leaves the compression damping for transient feel and control of the unsprung mass (correct?).

When I first specified the damper characteristic I didn't calculate damping ratios and only examined the results of the transient response simulation, with the basis that the non-linear damper characteristic would make examining the damping ratio useless. However, my current train of thought is to calculate the damping ratio for various damper velocities (i.e. points on the damper F(V) curve), while operating under the premise that the lower velocities will primarily be associated with the sprung mass and the higher velocities will have more to do with the unsprung mass.

I'll have to get back to you with exact numbers on Monday when I'm back home but for the time being here's a quick rundown my observations with respect to the rear suspension (the rear suspension seems to be more sensitive to the damping specification than the front, at least with respect to ride):

- When I was running into the odd harmonics related to tire stiffness the wheel rate was about 300 lb/in and I think the damping ratio turned out to be somewhere near critical.

- Using the same dampers with the same springs on a car with significantly stiffer tires (255/35-19? I'm not sure.), the ride and handling are good but I also got feedback from the driver that increasing the wheel rate by 25% still resulted in acceptable damping.

- Using the same dampers with softer springs (50-70% as stiff), as predicted by the quarter car model and realized through testing the sprung mass was overdamped (about 2 seconds to rebound to equilibrium following a displacement of approximately 2 inches - WOW!). The odd harmonic motion linked to tire oscillation was reduced, apparently resulting from a lower total load on the tires when the suspension was compressed.

- Another essentially identical car (BMW e36) with 17 inch rather than 16 inch wheels, a lower wheel rate (about 150 lb/in), and a damping ratio of about 0.7 worked well.

One caveat - I have yet to deal with the mediocre quality of the dyno data I have for the dampers. The first point was provided at 5 in/sec damper velocity and I am pretty sure there's no way the characteristic is perfectly linear in the range of 0-5 in/sec. Since the dampers are gas charged I suspect they essentially deliver no force in rebound up to about 1 in/sec, then the curve increases exponentially in the orifice region, until the blowoff comes into play. This agrees with some dyno results I have for the same type damper, taken by another guy. Since I have based my damping ratio calcs on the curves provided by the manufacturer, with no alteration, I wouldn't hang my hat on the resulting numbers.

At this point I agree with Greg's opinion that incorporating the tire stiffness is a good idea, especially considering I had bad results when I neglected it before.


Chris

 

[GregLocock]

Modelling damper behaviour in the 0-200 mm/s region is problematic. I have read an SAE paper where they did get good correlation, by building a fully detailed ADAMS model of the shock absorber. On a related note I know that a sufficiently accurate model of a hydraulic engine mount has something like 50 parameters.



Cheers

Greg Locock

 

[MoreWing]

Hutch,

I stuck the data that I pulled off the shock dyno in Excel so I could get an equation for the bump rubber rates. It turns out that they act in a cubic fashion. In these equations, the X is inches of compression and the Y is pounds of force. I only measured the first inch of compression.

Penske has 3 bump rubbers, Red, Tan, and Black.

Red: y = 203.12x3 - 216.94x2 + 130.86x + 3.4818

Tan: y = 184.15x3 - 196.48x2 + 138.64x + 3.4475

Black: y = 451.03x3 - 550.43x2 + 347.18x - 1.0979

Please excuse the ridiculous significant figures. It's a direct copy from Excel.

Like I said before, there is some damping in there, but not enough to write mom about.

On to the dampers. 0.7 critical is probably still a bit high. Try dropping it to 0.5-0.6, I bet you'll find a grip gain without losing much in terms of response. Until you've done a _bunch_ of running, stick with a linear curve. I might not be absolutely optimum, but you'll be suprized how close to optimum it will actually be. Bump is just as important as rebound, don't disregard it. You'll probably want different damping ratios in each direction.

You'll definitely want to know what the dampers are doing below 5 in/sec. That's where they spend the greatest portion of their time. Don't think that because of the gas pressure the shocks aren't doing anything in rebound at low speed. That's just another spring, nothing else. The damper will work at low speeds regardless of what the dyno says. Zero the curve at 0 shaft velocity if you want. That will give you a better idea of what is happening in the low speed regions of the curve.

The only thing that bugs me about putting tire data in the mix is the fact that you'll have dubious tire data at best. If you pick a single tire to run on, and then base all your calcs. off that particular number, then great. If you vary the tire around a lot, I can see you getting lost very easily.

Cheers.

 

[hutch325]

Thanks for the info on the Penske bump rubbers. Interestingly, taking the derivative of the equations indicates that the rate decreases then increases as a function of displacement. That's not meant to cast doubt on the numbers, it's just interesting to me.

I haven't had time to pull out all of my numbers on the various configurations but one interesting piece of information is that using the standard aftermarket Bilstein dampers and stock springs for the BMW in question, the calculations indicate the sprung mass is overdamped in the wheel velocity region of about 0-10 in/sec. That is consistent with the behavior of the car - no overshoot when it rebounds from about 1 inch of compression. Definitely a contrast to my co-worker's Jetta with stock suspension that has a couple overshoots, at least for the rear.

Let me take another look at the other configurations I examined to make sure I'm recalling the numbers correctly and also to do the calcs for damping ratios in compression. I feel like I have provided some disjointed information so far.

 

[GregLocock]

Are you talking about damping as a %age of critical? Milliken suggests around 15% for a production car, and 45% for handling.

In the UK the criterion of acceptability for shock abosrbers for roadworthiness is that the suspension should settle after one cycle. (ie release from down,up, down, settle).

The foam type of spring aid buckles as it compresses, this may give a lessening of rate, until the buckled material contacts the next fold.

Cheers

Greg Locock

 

[hutch325]

Yeah, damping as a fraction of critical. It looks like Milliken recomends 0.25 for a production car for ride and gives some examples of various damping ratios for race cars.

I'm not saying that from factory the car is overdamped, just what the calculations indicate for factory springs and aftermarket dampers for this particular vehicle. I don't dispute that it sounds too high and in fact I checked my calcs a number of times to try to find a mistake (I am kicking myself for not doing all my calcs in SI units from the get go). Nonetheless, the behavior of the car in rebound seems to agree with the calculation.

I can only speculate on what the damper manufacturer was trying to accomplish with the design. The car actually doesn't feel bad though. It feels firm and responsive but the ride is not harsh.

 

[BillyShope]

This seems pretty basic, but perhaps you're missing it:

Rubber is usually modelled as a damper in parallel with a spring and damper in series.

This makes sense when you remember the slingshot you made as a kid. You could hurl that rock a lot further if you quickly pulled back and released, as opposed to pulling, aiming, and releasing.

 

[MoreWing]

The spring rate curve of nearly all bump rubbers that I've tested has an initial stiff portion before going to a linear spring rate. I don't know exactly why. They are normally shaped like a cone, so I've attributed it to the geometry of the thing. The Penske's that I gave the numbers for have 'billows' that engage progressively as the thing is compressed. I assumed that was to keep it linear for a longer range of compression. The ramp-up at the end is common to all of the bump rubbers I've tested.

 

[Pneuride]

I make these polyurethane "Bump rubbers" you are referring too.

The rate of the part is determined by two things.

1) The density of the sample
2) The physical shape of the part.

In reality the physical shape has little influence other than bigger is better, typical features are hollow tops to give the soft start and aleviate the initial stiff portion.

The rate curve for the components are determined by the fact that they are cellular, the initial soft portion or linear area of the curve resulting from a combination of cellular and dimensional collapse, the block out at the end is when the cells are fully compressed and you have a solid mass.

Typical densities are at 0.5g/cc I'll give you some basic numbers for material rate (not including dimensional changes)

Strain % / Stress N/mm

20/0.49, 40/0.69, 50/0.9, 55/1.15, 60/1.48, 65/2.2, 70/3.8, 75/12.0.

I'll let you do your own conversions. I know its a while after thread death but thought you still might find the data useful.

Regards

Pneuride

 

[TravWood]

Again, It is a while after thread dates.

If you are after specs on Bilstein bump rubbers let me know a part number of the shock or insert and would be able to help you trace it. Send me details travers dot wood at bilstein dot com dot au I can't give you drawings but i am sure I will be able to give you some helpful numbers.

Also when you talk about chasing critical damping or portions therof at what shaft speeds are you talking about as many Bilsteins are not built with linear pistons although BMW generally seem to have them.

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