All sorts of natural frequencies

[Eager Learner]

Hello I love F1 and racing of any kind. I am new here, 16 years old, and hope to learn a lot from you wonderful people. I read a lot of this forum but now I have to register so I can ask questions to learn more!

1) Is it true that a car has a few different natural frequencies such as

Heave
Pitch
Roll
Warp

How are these frequencies calculated? If calculation is difficult due to exact masses and placement being unknown, what are some practical methods to measure this on a car if I have decent data acquisition?

How does one differentiate between sprung mass natural frequency and unsprung mass natural frequency? Again how do you calculate this, or at least measure it?

2) When a car is driving down a bumpy road at known speed and where the bumps are of a known frequency, how do we know which frequency we're supposed to damp for ideally, since it is not just the sprung mass oscillating, but the unsprung masses too. To further complicate it there is the tire natural frequency too, so how do we know how much to consider each of the 3 natural frequencies to give lowest contact patch load variation in this simple case of straight line?

3) Is tire natural frequency divided into lateral, longitudinal, vertical, and torsional? Do racing tire manufacturers give this data also?

4) I have read about yaw inertia, but is there a natural frequency for yaw for a given car on a given tire? As tire grip goes up and vehicle mass goes down, natural yaw frequency increases correct? Is there a practical way to measure this, assuming I have basic data acquisition on a car?


In terms of engineering a racing car for best lap time, which of all the natural frequencies are the most important to know either by calculation or measurement, and how is the information used practically to improve which areas?

Thank you for any help or information, you all are great!

[DaveW]

You haven't had many takers so far, I am afraid. The reason is that the questions you have asked would require a fair sized book to answer. Fortunately, there are many good books that could provide answers, but lets start with Wikipedia : for basics, & for general. In both cases the "See also" sections contain useful links.

To comment :

1. You might decide after rummaging around in this that Warp will not have a natural frequency, but that you have omitted Lateral & Yaw.

2. Vehicle modal responses are characterized by natural frequencies & damping ratios. It is the damping ratios that have a major impact on load variations.

3. In the context of the whole vehicle, tyres do not have natural frequencies (tyre engineers are sure to disagree with this, but they will be talking about "internal" modes).

4. Wikipedia might help here. Note the references.

I hope this helps.

[Richard]

Thanks DaveW, I saw this but unfortunately it was well outside my scope.

[Belatti]

Dave, I have some translation problems to figure out what is what you call "warp". Can you enlighten me?

[DaveW]

Warp:

1. to bend or twist out of shape, especially from a straight or flat form, as timbers or flooring (dictionary.reference.com)

It is a term "borrowed" from structural distortion. If corners are ordered front left, front right, rear left, rear right, then

Heave = Amp*[ 1, 1, 1, 1]
Pitch = Amp*[ 1, 1,-1,-1]
Roll = Amp*[ 1,-1, 1,-1]
Warp = Amp*[ 1,-1,-1, 1]

Hope that makes sense.

[Richard]

Warp could also be [ 1, 1,-1, 1] ? Ie one corner dropping, as well as opposite corners

[DaveW]

Warp could also be [ 1, 1,-1, 1] ? Ie one corner dropping, as well as opposite corners

It's all about convention. Your vector would be equal to 0.5*(H+P-R+W) in my notation

[Belatti]

got it! Thanks!

[GSpeedR]

You will find that every independent degree of freedom will have a mode of vibration (assuming it has some mass/inertia, of course), the first mode is referred to as the natural frequency or natural mode. Simply the fact that these modes exist does not necessarily mean that the vehicle conditions will excite them, and it is often quite difficult to measure them outside of the laboratory. You may need a special rig to excite these modes and with an appropriate bandwidth; the road or racetrack is often not the best place to characterize. However, if you have a lot of time and a set of accelerometers, there's no harm in logging track data and analyzing the data; most data acquisition software can do (at least) basic frequency domain analysis.

[WilO]

This question probably has a very obvious answer, but what vehicle properties contribute to the lateral natural frequency? I would assume that tire characteristics would be significant determinents, but I'd be grateful for additions and corrections.

Wil

[DaveW]

....

[DaveW]

This question probably has a very obvious answer, but what vehicle properties contribute to the lateral natural frequency? I would assume that tire characteristics would be significant determinents, but I'd be grateful for additions and corrections.

Your question is not easy to answer, Wil.

Assuming that the roll mode responds to a roll input in a "decoupled" way (no other modes are excited), then the centre of roll will be (roughly) through the centre of gravity. Hence, with a "normal" vehicle layout, roll displacement requires the wheel hubs to move laterally relative their contact patches. It follows that tyre lateral compliance will generate forces acting on the vehicle when the wheels are stationary (as in a rig test), and they will affect the roll mode natural frequency. The situation changes when the wheels are rotating, when tyre "relaxation" allows the tyres to deflect with (much) reduced lateral forces. It is normal to neglect tyre lateral forces in this case and, with no damping, infinite vertical tyre rate (& recalling my assumptions - particularly the first one), the natural frequency of the roll mode will be proportional to the roll stiffness of the combination of spings & bars divided by the roll inertia of the sprung mass.

It is fair to say, however, that the above computation would produce an estimate of roll natural frequency which would be some way from reality. In most realistic cases structural layout, geometry, springs, dampers and vertical tyre stiffness will mean that roll displacement is usually coupled with lateral & yaw defections, which can have a significant effect on both natural frequency & damping ratio of the roll mode. This, when combined with tyre non-linearities (particularly when they start to slick-slip) can cause some quite interesting instabilities involving tyre lateral stiffness, even when the tyres are rotating. In those cases, rig testing (with static tyres) can be instructive....

I hope this makes some sense....

[WilO]

Dave,

Thank you, that helps a great deal, as I clearly didn't have much of an idea....though it doesn't seem to be a topic discussed in many texts.

Thanks again, great information as always.

Wil