Calculating Rigid body motion from accelerometer data
Calculating Rigid body motion from accelerometer data
(OP)
Hello all,
I was hoping to get some feedback/advice from the group.
I have a frame for which I would like to get a much better handle on what is going on with it.
I have 3-axis acceleration data at 5 locations on a frame with respect to time (about 60 seconds worth). What I am trying to calculate is how to represent the frames motion over time given the acceleration data. For now, I am going to keep it simpler, by assuming planar motion (setting aside the z accelerations for now). (let X be parallel to ground, and Y vertical, with Z perpendicular to long axis of frame)
I pulled out my old dynamics text, and I THINK that I am going to need at least 3 of the accelerometers data to be able to obtain the general,planar motion of my "rigid" body.
I'm looking at a chapter labeled "Relative-Motion Analysis:Acceleration"
To state the acceleration of a point on a rigid body, you relate it to another points acceleration and the relative acceleration of the two. I will need to know alpha (angular acceleration of the rigid body), and omega (angular velocity of the rigid body). Obviously, I know the relative position vectors, as I know where the accelerometers were put.
A1 = ACG +A1/ACG = ACG + (alpha X r1/CG) - (omega^2*r1/CG)
A5 = ACG +A5/ACG = ACG + (alpha X r5/CG) - (omega^2*r5/CG)
A3 = ACG +A5/ACG = ACG + (alpha X r3/CG) - (omega^2*r3/CG)
here,
A1, A3, A5 = accelerations at point 1, 3, and 5.
ACG = acceleration at the frames center of gravity.
alpha = frames angular acceleration
omega = frames angular velocity
r1/CG, etc = position vector from point 1 to center gravity
Does this look correct to everyone? I appreciate your thoughts, Thanks!
I was hoping to get some feedback/advice from the group.
I have a frame for which I would like to get a much better handle on what is going on with it.
I have 3-axis acceleration data at 5 locations on a frame with respect to time (about 60 seconds worth). What I am trying to calculate is how to represent the frames motion over time given the acceleration data. For now, I am going to keep it simpler, by assuming planar motion (setting aside the z accelerations for now). (let X be parallel to ground, and Y vertical, with Z perpendicular to long axis of frame)
I pulled out my old dynamics text, and I THINK that I am going to need at least 3 of the accelerometers data to be able to obtain the general,planar motion of my "rigid" body.
I'm looking at a chapter labeled "Relative-Motion Analysis:Acceleration"
To state the acceleration of a point on a rigid body, you relate it to another points acceleration and the relative acceleration of the two. I will need to know alpha (angular acceleration of the rigid body), and omega (angular velocity of the rigid body). Obviously, I know the relative position vectors, as I know where the accelerometers were put.
A1 = ACG +A1/ACG = ACG + (alpha X r1/CG) - (omega^2*r1/CG)
A5 = ACG +A5/ACG = ACG + (alpha X r5/CG) - (omega^2*r5/CG)
A3 = ACG +A5/ACG = ACG + (alpha X r3/CG) - (omega^2*r3/CG)
here,
A1, A3, A5 = accelerations at point 1, 3, and 5.
ACG = acceleration at the frames center of gravity.
alpha = frames angular acceleration
omega = frames angular velocity
r1/CG, etc = position vector from point 1 to center gravity
Does this look correct to everyone? I appreciate your thoughts, Thanks!





RE: Calculating Rigid body motion from accelerometer data
For 2d motion you need to measure X and Y vibrations at two points only, and if you choose the directions sensibly, one of those is redundant.
Again for 3 d motion you'll need 3 locations, but you won't need x y and z at every one, there is some redundancy there.
Cheers
Greg Locock
RE: Calculating Rigid body motion from accelerometer data
So on this occasion, I disagree with Mr. Locock.
RE: Calculating Rigid body motion from accelerometer data
RE: Calculating Rigid body motion from accelerometer data
I have set up the data in a MathCad worksheet and using two sets of accelerations, I appear to be getting reasonable accelerations as functions of time. I am using these values to approximate wheel loading on my frame.
Coincidentally, I did an FFT on the data, and I am getting peaks at frequencies which correlate to those I calculated given a "rigid" frame, and tires having a given stiffness. (Had to go way back to advanced vibs days for that calculation). There is one more peak that is showing up in the frequency domain, but my suspicion is that it is the frame's first natural frequency. As soon as I have a chance, I will come up with an approximate number on this.
There is also seeming to be a consistent broadband response at the low frequency end (zero to 5'ish Hz). This I would presume is the response from repeated holes, bumps, edges, etc?
So, the data, from a big picture sense seems to be following what I would "expect", making me believe I am on the right track here. Thanks again!
RE: Calculating Rigid body motion from accelerometer data
So its got "tires" huh ?
By the way - I didn't mean to imply you weren't following it - just that there seems to be a general lack of response - not even a follow up from Mr. Locock about his "middle column". Now that the subject of FFT's has come up he'll probably respond.
RE: Calculating Rigid body motion from accelerometer data
I'd say the FFT analyser is usually OK down to DC typically (after all if you switch high pass filtering off they make perfectly good if rather expensive voltmeters), the problem is that the rest of the instrumentation is not capable of reliably responding at low frequency - most piezo accelerometers chop out at about 3 Hz, and charge amps the same. It is possible to buy DC accelerometers - based on strain gauges. They are fragile, but a delight to calibrate, since you just turn them upside down to get a 2g offset.
These low frequency cutoffs are not especially well defined, although I think B&K gear still gives you good linearity between channels at 3 Hz, even using different accelerometrs and charge amps.
Typical road surfaces have a 1/f spectrum which probably explains the LF stuff.
The best way of getting RBMs from a wheeled vehicle using operational data is to run at high speed on a smooth road, and fix an out of balance weight to one wheel. Then do a coast down and synchronous sampling. Clean data!
Cheers
Greg Locock
RE: Calculating Rigid body motion from accelerometer data
RE: Calculating Rigid body motion from accelerometer data
With a strain gauge you can see this down to zero - it is how we calibrate them.
I don't know why piezos roll off at low frequency, it could be the charge amps. I can't see an intrinsic reason.
The roll off still happens - we get a lot of signal at 1-2 hz as that is primary ride in a car, and the piezos are great at filtering it out!
Cheers
Greg Locock
RE: Calculating Rigid body motion from accelerometer data
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