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# Vehicle dynamics: rigid modes PSDs question

## Vehicle dynamics: rigid modes PSDs question

(OP)
Hi all,

I performed some measurments of pitch, roll and bounce accelerations of a vehicle. I installed three accelerometers placed as a triangle and through few trivial formulas (ie roll_acc=(a_lh-a_rh)/(2*l), where l is the distance between the accelerometers and a_lh and a_rh are the accelation at two sides of the vehicle) I derived the vehicle pitch, roll and bounce accelerations. I drove the vehicle on a straight asphalt road.
These are the PSDs of the mentioned signals.

http://img690.imageshack.us/img690/6311/40024043.jpg

What seems strange to me is all the PSDs have a peak around the same frequency (2.25) . May you be so kind to explain to me the reason of that?

Best regards

### RE: Vehicle dynamics: rigid modes PSDs question

You've given nothing in the way to indicate whether this is an artifact or real.  If real, it may be a suspension mode.

### RE: Vehicle dynamics: rigid modes PSDs question

(OP)
I'm sorry, but I don't have any idea about the kind of information you could need.. Let me know which kind of information you need. I performed this measurments on a dozer, so no suspensions, pivoting front axle, rear rigid axle and different tyre sizes. Could it be possible the rigid modes are coupled? Like the roll could generate a pitch since the tyres have different sizes and so different stiffnesses.

Thank you

### RE: Vehicle dynamics: rigid modes PSDs question

I think it is a bit more subtle than that. Human beings think in terms of pitch roll and bounce. Real systems don't. There is absolutely no chance that a real untuned vehicle will exhibit pure pitch, pure roll, and pure bounce modes.

In reality you'll have a mixture of at least 2 dof in each mode, for instance in a car the two pitch bounce modes are often described in terms of the location of the node in the x axis.

So in terms of axle deflections where you might expect 1,1 for the bounce mode and 1,-1 for the pitch mode, in reality you get something more like 1,-1.3 and say 1,0.5 .

So you need to decompose your vibrations into the actual mode shapes, which you can do by some sort of least squares approach i guess.

Cheers

Greg Locock

New here? Try reading these, they might help FAQ731-376: Eng-Tips.com Forum Policies  http://eng-tips.com/market.cfm?

### RE: Vehicle dynamics: rigid modes PSDs question

(OP)
Dear Greg,

thanks for your reply. I get it. I thought it was always possible to decompose a general vehicle movement to a composition of pure pitching, a pure bouncing and a pure rolling but I understood it depends by the vehicle parameters.
I measured the seat acceleration and I would like to undestand the contributions of each modes on the seat acceleration. In other words my question is: does the pitching affect more the vertical seat acceleration than bouncing? Is it possible to accomplish it, through your proposed method?
Any suggestion is appreciate

thank you again

Best regards

Pietro

### RE: Vehicle dynamics: rigid modes PSDs question

You CAN decompose the motion, but measuring and validating your measurements is a different matter.  Taking differences of two measurements is a tricky proposition at best.  Your apparent angular content may be nothing more than measurement phasing differences between the sensors.

I suggest that you consult the ISO standards for vehicular motion.  Angular disturbances can be worse than linear disturbances, but your measurements are showing about 1°/s^2 rms, which may be a problem for an electro-optical imaging system, but is probably very benign for a rider.

Again, you've not indicated what the conditions were for the data collect.  Don't you think that information would be pertinent?  Was the course ultraflat and level?  Was it a Perryman or Churchville test track?  What speed was the vehicle moving at.

### RE: Vehicle dynamics: rigid modes PSDs question

(OP)
Dear IRstuff,

Thanks for your reply, I drove the vehicle on a normal straight road at 30km/h, which was the speed where the seat suspension works in resonance. The road was quite flat for being a normal road, but not as good as a test track. I also drove the vehicle on standard  rough track  (ISO 5008 is the standard for the track surface definition) used for evaluting the ride vibration for off-road vehicle. But the shown PSD is from on road driving. I know the IS0 7401, 4138, 13674-1 and 8726, but they don't seem useful for what I want to get. Do you know other ISO standards?

thanks!

### RE: Vehicle dynamics: rigid modes PSDs question

I don't do this for a living, but I would be more inclined to use gyros for measuring angular motions.  Linear accels have been successfully used for measuring angular motions, but not without a considerable amount of work to ensure simultaneity of the data differencing.

Again, you need to review how the measurements are being made.  It seems highly unlikely that roll and pitch would have the identical resonance frequencies, since the lever arms are different.  Furthermore, your measurements show roll have less power content than pitch, which would seem to be unusual for a vehicle on a flat road.

Even the linear accel seems suspicious to me.  The PSD works out to something on the order of 0.2 g rms, which seems awfully bumpy for a flat road.

### RE: Vehicle dynamics: rigid modes PSDs question

(OP)
IRstuff,

In reality we bought two inertial platform for the new measurments, but I want to understand more the old measurments I did.

By the way, the vehicle I used doens't have any suspension system, the wheels aren't equilibrated, their CoGs aren't placed in their axis, so  should it be possible, the pitch acceleration has more power than the roll acceleration, right? Regarding to the roll main frequency, I think roll and pitch can be coupled since fron wheels have a different radial stiffness than the rear ones, so the front tyre deflections are different than in the rear.

You wrote: " The PSD works out to something on the order of 0.2 g rms, which seems awfully bumpy for a flat road. ". So which estimator is better than the PSD for getting the spectrum?

thanks

### RE: Vehicle dynamics: rigid modes PSDs question

I'm not saying that PSD is the wrong venue, I was questioning the data itself, even the linear accel stuff, but maybe an unsprung vehicle would have that behavior.

Nonetheless, I was still expecting that it would be easier to get a vehicle to roll than pitch, since the moments of inertia are quie different.

### RE: Vehicle dynamics: rigid modes PSDs question

my point about decomposing the motion to pure pitch roll and bounce (which is certainly possible and may even be useful) is that each of those pure shapes will have contributions from each of the 6 rigid body modes, and if you have a powerful mode at 2.25 Hz it will show up in all of your assumed modes.

Also since you ran at constant speed there may be an excitation from that, so you may be seeing a forced response.

Cheers

Greg Locock

New here? Try reading these, they might help FAQ731-376: Eng-Tips.com Forum Policies  http://eng-tips.com/market.cfm?

### RE: Vehicle dynamics: rigid modes PSDs question

(OP)
Hi all,

Greg this is the PSD while running on a straight road from 10 to 40km/h.

http://imageshack.us/f/26/provaof.png/

As you can see the strongest PSD peaks are still at 2.25Hz, so this graph should demonstrate, this peak is due to a vehicle mode, right?

IRstuff, you're right, but an unsuspended vehicle is quite sensitive to wheelbase filtering effect, and wheelbase is much higher than track, so in my opinion it should be possible that pitch has more power than roll

### RE: Vehicle dynamics: rigid modes PSDs question

You can't tell, it could be a forced response. There are some hints that it is not a forced response, lack of 6.7 Hz for a start.

I can't tell if you understood my point about residual effects of the actual modes on your assumed modeshapes. I think that is the key.

Cheers

Greg Locock

New here? Try reading these, they might help FAQ731-376: Eng-Tips.com Forum Policies  http://eng-tips.com/market.cfm?

### RE: Vehicle dynamics: rigid modes PSDs question

Sorry, i'd forgotten it is a sped sweep. I agree the chances are that you have a strong 2.25 Hz resonance, what we don't know is the actual mode shape.

Estimating mode shapes from operating data is difficult, but not impossible. Often we select one vertical acclerometer channel to be the 'reference' and then we take transfer functions between that and the other channels, as if it were a modal analysis.

It's crude and nasty. And it works as often as not.

Cheers

Greg Locock

New here? Try reading these, they might help FAQ731-376: Eng-Tips.com Forum Policies  http://eng-tips.com/market.cfm?

### RE: Vehicle dynamics: rigid modes PSDs question

(OP)
Greg,

I got your point and I agree with you. I don't understand how I can calculate the effect of pitching and bounce on the seat acceleration for understanding: is much more important to minimize the pitching or the bouncing?
Maybe the composition in modes would be useful, but probably I would get the pure modes.

thanks

### RE: Vehicle dynamics: rigid modes PSDs question

Didn't you ride the vehicle during the data collect?  How bad did it feel?  Is it even noticeable?  The bounce on your last image seems to be less than 0.1 g rms, and angular seems to be less than 0.1° rms.  Is that really a big problem?

### RE: Vehicle dynamics: rigid modes PSDs question

(OP)
Dear IRstuff,

I drove the vehicle, and it was really uncomfortable. The acceleration level was much higher the limit value prescribed by the European directive.  Morever al PSD are in terms of acceleration, even the angular ones. Maybe this could explain to you the reason of low amplitudes.

Thanks

### RE: Vehicle dynamics: rigid modes PSDs question

"uncomfortable" seems inconsistent with your data, which also seems inconsistent with being over any sort of threshold, but I'm not familiar with them so...

What level does this directive require?  Where on the vehicle are you making these measurements?

### RE: Vehicle dynamics: rigid modes PSDs question

(OP)
Dear IRstuff,

why are you saying my data are incosistent? As far as I know, without the sample number is hard to understand amplitudes from the PSD, right?

The European directive require a maximum of 1.15 m/s^2 of vibration level measured at the seat in according  with the standard ISO 2631-1. In this standard it must be measured the seat  accelerations along the three axis-> apply a frequency weighting function-> calculate the RMS values of each of them-> the vibration level is:
sqrt[(1.4*Ax,rms)^2,(1.4*Ay,rms)^2,Az^2)]

I was on the vehicle.

Thanks

### RE: Vehicle dynamics: rigid modes PSDs question

The measurements you show, only for z-axis, is only about 0.11 m/s^2, rms, which is well below your stated standard, and would seem to be a very benign ride.  Something that is uncomfortable, would be more likely to be in the range of 0.5 m/s^2 and upwards.

### RE: Vehicle dynamics: rigid modes PSDs question

I got a units problem when I looked at the plots, the vibration appeared to be in (m/s)^2

Anyway, the passenger is primarily sensitive to what s happening to him, and that is the vertical input from the seat, and longitudinal on the back of the seat. Pitch and roll are secondary.

Cheers

Greg Locock

New here? Try reading these, they might help FAQ731-376: Eng-Tips.com Forum Policies  http://eng-tips.com/market.cfm?

### RE: Vehicle dynamics: rigid modes PSDs question

normally, it would have been (m/s^2)/sqrt(Hz)

### RE: Vehicle dynamics: rigid modes PSDs question

(OP)
Hi all,

sorry for the unit problem. I calculated the psd from a linear acceleration in m/s^2 and from an angular acceleration in °/s^2.

IRstuff, how do you guess the rms value from a PSD?

Greg, Look at this reasearch report http://www.hse.gov.uk/research/rrhtm/rr321.htm page 66 fig 5.8. The vertical acceleration is always lower than the horizontal ones, due to ISO standard post-processing. The vibration level at the seatbase is always lower than the one at the seat. In my opinion this is due to the tractor angular accelerations and I want to evaluate somehow their effect on the seat accelerations. Since the seat is rigid on the horizontal directions, the seat linear acceleration due to the pitch is: pitch acceleration times the vertical distance between the pitch center and the seat position. The same with roll.
What do you think? Any other suggestions are appreciated.

Thanks again.

### RE: Vehicle dynamics: rigid modes PSDs question

You're supposed to do the numerical integration across the entire bandwidth, but seeing as it's only picture, my "guess" was a brute-force eyeball integration of curve.

"The vibration level at the seatbase is always lower than the one at the seat. "

That's troubling; a properly designed seat, particularly for a vehicle with no suspension, is supposed to attenuate the vibrations so that the passenger receives an attenuated vibration.  It's also possible to design the seat to minimize angular motions, and it should certainly not create more motion than the vehicle generates.

### RE: Vehicle dynamics: rigid modes PSDs question

Well that would be in the ideal world. In practice the resonance of the human body on the seat does cause some pretty neat resonances, at least on passenger car seats.

Cheers

Greg Locock

New here? Try reading these, they might help FAQ731-376: Eng-Tips.com Forum Policies  http://eng-tips.com/market.cfm?

### RE: Vehicle dynamics: rigid modes PSDs question

(OP)

IRstuff: I don't want to design a seat suspension to minimize the angular motions, I think it's better to decouple systems so to design a cab suspension to minimize the angular movements. But the first question is: which rigid modes it's better to minimize?
Tractor cab have this kind of suspension system:

that it is designed to minimize pitching.

Greg: you're on right.

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