Post rigs

[Belatti]

I wont tell you that track surface simulation in a post rig is useless, but I fail to see the benefits of it, other than cheking system integrity.

The most popular use for post rigs I know (take into account here in Argentina they are underdeveloped in comparison to those of Europe or the US) is working with frequencies "scanning" (what would be the word in English for these??). And to select the apropiate frecs and strokes combinations is way easily than trying what you intend to do

[Greg Locock]

So we came up with the idea to reverse engineer the damper displacement per wheel into a possible(!) road surface, since actual track data is unknown. I filtered the signal to get rid of displacements due to e.g. cornering and aero. I initially created a Simulink Quarter Car Model, analytically derived the transfer function of the system and the State-Space system. Of course, things like sprung and unsprung mass, spring stiffness, tyre stiffness, damper characteristics are known. However, I did not find a method how to invert the transfer function such that the damper displacement can be used as a "input" to the system, yielding a possible track surface as output. Could anyone help me solving such a reverse engineering problem or give an advise how to tackle it?

I think you've out-thought yourself. There's no guarantee that a transfer function like this can be inverted easily. So what you do is run your shock displacements into your simulink model, and keep the timehistory of the contact patch motion and use that to drive your rig. Then monitor the actual shock displacement on the rig (which should in theory be the same as what you originally measured) and adjust the drive signal to compensate.

It will be a lot of work to get that last bit right. You have to make assumptions about the tire that don't seem to work in practice when the Test guys do it for 4 poster rigs.

What my Vehicle Dynamics colleagues do is to measure the profile of the road surface and model it in CAD. Then I run it into an ADAMS model and can more or less predict what is going on up to 5 Hz (which is what I am doing on a rainy Saturday morning).

[DaveW]

Greg and Belatti are both correct.

Commercial 7 post rig suppliers provide proprietary methods to accomplish the task. MTS use "RPC", Instron-Shenck use "Spidar", & I cant recall the name (if any) of the Servotest routines.

The idea is that you extract a lap from a track recording taken with the vehicle in a known state. Then install a vehicle in the same state on the 7 post rig (ideally the same vehicle), and run an iterative identification routine, generating drive files for the various actuators to minimize the differences between selected track and wheel measurements, after the deterministic response components have been accounted for.

This sounds simple & logical, but it isn't, for a variety of reasons which I will gloss over for now. It is usually the case that the drive files are highly dependent on the transducer set chosen as reference. If damper positions are chosen as reference, for example, then PRL won't match. If PRL are chosen, then damper positions won't match. Choose both, & the iteration refuses to converge.

Modelling the task is even more difficult, because the basic model first has to be validated, and a decision taken about inevitable differences between the model & the vehicle. A simple example would be sprung mass value. It is normal to assume that the sprung mass is a monolith, but that is not the case in reality (the apparent mass increases measurably with input frequency).

At any rate, if you choose to ignore the above, then MatLab Identification Toolbox has several tools that might help to generate drive files, including MMLE3, I believe.

EDIT: I wrote the above without first validating my memory - apologies. This, however, might be more helpful. Look up the Academic Publications menu item.

[Belatti]

Thinking about what you wrote Dave, I see that Im in a point in postrig development here where the mere fact of using it improves track parformance. In my case, what works for me is to dissect damper pot signal from preponderant combined Gs and analyze it. With that I generate different drive files for specific track sectors. At the end, as always, compromise solution. Maybe a more rudimentary and "home made" process...

EDIT: I wrote the above without first validating my memory - apologies.

[DaveW]

Belatti: I once wrote, without trying to be controversial:

Four Post Tests:

> Good for identifying setting limits, vehicle properties and deficiencies.
> Good for optimising linear range suspension settings.

Seven Post Tests (short for "Track Simulations"):

> Good for setting packer gaps, spring preloads (realistic input amplitudes) and exposing damper deficiencies (cavitation).
> Can be poor for setting dampers (downforce actuators can act as “skyhook” dampers).

Neither can:

> Optimise driver/vehicle compromise.
> Set the mechanical lateral balance of a vehicle.

About sums it up, I think....

[Belatti]

No controversy at all! I use a 2 post rig for the same purpose of the 4 post you wrote. Then I do "manual" drive files taking into account "relevant" (for me) track parts data, ignoring for the sake of practicality, the track data from straights (low combined G)

[olefud]

This has been mentioned but not discussed –what about (non)spinning wheels? It would seem that the main concern is gyro force inputs orthangular to wheel movement that load suspension members and bearings, i.e. stiffen the suspension. Is this a concern?

[GSpeedR]

Hi guys, as a passive reader of this forum, I found myself in a problem in which you might be able to help.

For the sake of virtual seven post rig shaking, I am trying to generate a road surface input for our virtual shaker. We used to use a random white noise signal, but optimizing damper settings on such a road is not useful for racing real circuit.

So we came up with the idea to reverse engineer the damper displacement per wheel into a possible(!) road surface, since actual track data is unknown. I filtered the signal to get rid of displacements due to e.g. cornering and aero. I initially created a Simulink Quarter Car Model, analytically derived the transfer function of the system and the State-Space system. Of course, things like sprung and unsprung mass, spring stiffness, tyre stiffness, damper characteristics are known. However, I did not find a method how to invert the transfer function such that the damper displacement can be used as a "input" to the system, yielding a possible track surface as output. Could anyone help me solving such a reverse engineering problem or give an advise how to tackle it?

I assume that the 'transfer function' you have created is an S-domain (Laplace domain) transfer function and I also assume that your desired damper displacements are track-derived. The latter means that you will have serious difficulty performing Laplace transforms on your desired data (damper displacements), so I would recommend working primarily in the Freq domain (using FFTs). If you plan on continuing to use linear time-invariant components (ie linear spring/shocks/etc) then you can substitute s=j*w in your transfer function to obtain a Frequency Response Function, which will be a slice through the imaginary plane (real-part = 0) of your S-domain TF.

Y(w) = H(w)*X(w) ===> X(w)=invH(w)*Y(w)

where X(w) is the Fourier Transform of your Road Profile, invH(w) is your inverted FRF and Y(w) is the FT of your damper displacements. You must then transform X(w) -> x(t) using inverse FFT. Note that using real data (damper pots) means that you'll have to make assumptions about the data (infinitely long and periodic), which will require windowing and filtering. I would recommend a text on random vibrations if you are having trouble.

Many people refer to a FRF as a Transfer Function and maybe you have also, but I try to distinguish them when possible. With real systems, or even virtual systems with nonlinear components, there is significant effort involved in creating the FRF, and as mentioned above there is no guarantee that it can be inverted. If it can't, then the characterization process (to make the FRF) must be changed and then it is tried again. Otherwise you have to change the system, change the transducer type/location, change the rig, or give up.

It sounds like you have your TF and are happy with it, but you are not sure how to invert it(?). As long as your system is properly derived from equations of motion with ideal elements then your TF should not be singular, and thus it should be easily inverted using any matrix solver (ie Matlab): 'pinv' creates a psuedo-inverse and can handle non-square matrices, unlike the 'inv' function. However, if your TF is singular then you should look for mistakes in your equations or in the resulting matrices that make up your State-Space system. For example, do your mass, stiffness and damping matrices have equal cross-terms, and if not does this break energy conservation? As long as your degrees of freedom are independent and the elements are physically realizable then your resulting TF should be non-singular.

[DaveW]

I really do recommend that you consult the reference I listed earlier and visit the Academic Publications, particularly this one.

[DaveW]

This has been mentioned but not discussed –what about (non)spinning wheels? It would seem that the main concern is gyro force inputs orthangular to wheel movement that load suspension members and bearings, i.e. stiffen the suspension. Is this a concern?

All approximations are a concern, but I think non-rotating wheels is not a "show stopper", despite rumours to the contrary. It is a fact that tyres are not springs (or any combination of linear springs & dampers). The "tangent" vertical rate of a tyre is a function of temperature, pressure, input amplitude, mean load, frequency, loading "history" and, no doubt, wheel speed. Personally, I would not include gyroscopic forces in the list - but what do I know. It also appears to be true that lateral and vertical characteristics "follow" one another.

Whilst tyres demonstrably affect car set-up, the remarkable thing is an "optimal" the set-up doesn't change much with large changes in ambient conditions (e.g. the optimal damper settings for hot tyres is usually with a sweep or two of the optimal settings with cold tyres). I assume that this is because front & rear tyres are either the same, or compatible constructions & compounds.

More could be said on the subject, but I will stop at this point....

[GSpeedR]

I really do recommend that you consult the reference I listed earlier and visit the Academic Publications, particularly this one.

I have heard of iteratecontrol, but have not read any of their papers (thanks for the link, reading them now). My previous post loosely describes the 'inverse algorithm' (Equation 2 in the link), and, as mentioned, there are numerous caveats and deficiencies. However, RemcoA has never mentioned that an actual test rig will be used and he hasn't described anything other than a LTI State-Space model of a quarter-car system (2DoF). I think the inverse algorithm is perfect for this case since the FRF is ideal and should perfectly represent the ideal system. If RemcoA seeks to extend his model to include nonlinear elements or (better yet) collect data on a real system, then the links DaveW provided would definitely be beneficial.

[DavidO]

There are several iteration SW products on the market, most of which use a variant of the inverse algorithm. The inverse algorithm can solve many of these problems very efficiently but the hard mathematical fact is that several things can cause the inverse model iteration process and hence the test to fail.
These failure mechanisms include (1) errors in the frequency-based FFT or state space model as a representation of the rig, (2) substantial unmodelled nonlinearity and, less well known, dynamical properties of the rig and specimen. This last one is difficult to quantify and can be difficult to eliminate but is often linked with inversion of models which are almost singular e.g.what appear to be small modelling errors at the frequency where this problem occurs can "flip" the phase and, in effect, replace a stabilizing "negative" feedback effect with a destabilizing "positive" effect.
The Iterate Control software uses a "generalized algorithm" which replaces inversion with an alternative approach that can considerably improve robustness of the iteration process to effects such as these three and gives the user a greater degree of influence on performance in practice. It claims to provide a degree of control on the overall rate of convergence and allows the user to influence the relative rates of convergence in different channels.

[DaveW]

There are several iteration SW products on the market.

Good & informative post. Links, if available, would be appreciated.

[Greg Locock]

My previous post loosely describes the 'inverse algorithm' (Equation 2 in the link), and, as mentioned, there are numerous caveats and deficiencies. However, RemcoA has never mentioned that an actual test rig will be used and he hasn't described anything other than a LTI State-Space model of a quarter-car system (2DoF). I think the inverse algorithm is perfect for this case since the FRF is ideal and should perfectly represent the ideal system. If RemcoA seeks to extend his model to include nonlinear elements or (better yet) collect data on a real system, then the links DaveW provided would definitely be beneficial.

How can you work in the frequency domain, usefully, if the shock characteristic is non linear with velocity? If you have jounce bumpers? If you have rebound springs?

[Caito]

My previous post loosely describes the 'inverse algorithm' (Equation 2 in the link), and, as mentioned, there are numerous caveats and deficiencies. However, RemcoA has never mentioned that an actual test rig will be used and he hasn't described anything other than a LTI State-Space model of a quarter-car system (2DoF). I think the inverse algorithm is perfect for this case since the FRF is ideal and should perfectly represent the ideal system. If RemcoA seeks to extend his model to include nonlinear elements or (better yet) collect data on a real system, then the links DaveW provided would definitely be beneficial.

How can you work in the frequency domain, usefully, if the shock characteristic is non linear with velocity? If you have jounce bumpers? If you have rebound springs?

You could have several transfer functions, or you could linearize your system around an operating point.
At least that's what you do, but this has nothing to do with Post Rigs.