# French Passenger Train Vibration

I recently rode in the above French TER, Electric Train, Model Z 24500, Lyon to Annecy.

A sample accelerometer time history is shown above.  The sensor was mounted on a passenger car floor, a Slam Stick X, sampled at 400 samples/sec.

The spectrogram of the accelerometer data shows a cluster of peaks from 1 to 2 Hz.  These are mostly likely due to the interaction between the wheels and the track joint gaps.  The track length and the train speed would need to be identified in order to resolve this.    But here is a rough estimate using assumed values for speed and length:

speed/length = (25 m/sec) / 20 m = 1.25 Hz

Minor speed variations would cause the peaks to have some drift.

Some intermittent peaks also occur near 8 Hz.  Here is another rough calculation.  Assume that the wheels have a 1-meter diameter, with a circumference of pi meters.

speed/circumference = (25 m/sec) / (pi meters) = 8 Hz.

So the peaks near 8 Hz appear to be due to wheel static imbalance.

Also note that the electrical power frequency is 50 Hz, so the engine may have a component at this frequency.

Matlab Data:  French_train.mat

– Tom Irvine

## 1 thought on “French Passenger Train Vibration”

1. Hi Tom,

Hope things are well with you. My expertise falls toward the freight side of railroad dynamics, but I’ve done some passenger work over the years. If I may, I would offer these alternative suggestions about those particular peaks.

The nominally 1 Hz response is most likely a kinematic lateral mode due to the coned tread of the solid wheelsets called carbody hunting, although it is quite subtle as that mode of response goes. A secondary possibility here would be carbody (sprung mass) bounce on the truck (bogie) suspension. The vast majority of modern track is CWR (continuously welded rail) not jointed, laid in sections about 1700 feet long. So there are likely few joints to provide the forcing function (again with a caveat, sometimes locally the earth has taken on an irregular vertical stiffness due to past joints and can still provide some 39-ft wavelength input energy).

The 8 Hz component may be unbalance, but as well, the wheels don’t start perfectly round and can develop sheel or spall discontinuities on the tread causing veritcal periodic energy once/rev.

The 50 Hz component most likely reflects the non-constant vertical stiffness of a rail-on-crosstie track at the passing frequency of the crossties (sleepers), Between ties, the rail bending stiffness controls the vertical support, while at the ties the stiffness is mainly due to the supporting ballast conditions.

David Thompson’s book “Railway Noise and Vibration” is the most complete treatment of the subject, but as well Iwnicki’s “Handbook of Railways Vehicle Dynamics” is excellent. A brief introduction is in this: http://www.railtec.illinois.edu/CEE/pdf/PPT%27s/previousppts/univ_illinois_shust.pdf which are the slides from a graduate seminar that I was invited to give several years ago. As always, your many contributions to the field are excellent and most interesting. -bill s.