Interesting, I've always known that recips have a torque oscillation, but I haven't seen it quantified like this.
Out of curiosity, what is the source of these torque spectral values? Was it measured somehow? How/where
fwiw, I'm still inclined to think the vibration on the motor (at multiples of running speed) is a result of the torque variation of the load (at multiples of running speed). If you want a higher degree of confidence you can do some more investigation. Try uncoupled run of motor. Perhaps check for obvious mechanical looseness at bearings / housings / support structure since these can be alternate source of harmonics of running speed.
My attempt to respond to your individual questions:
1. your reactions points to loose stators. Are the attached harmonics so typical?
2. can we exclude external sources or the electric net as possible orign at first?
3. can a bent shaft (not stiff enough) generate such an spectrum?
4. Actuall we have 2 motors with same issues. should we consider really a loose stator from the beginning of operation.
That points to a more fundamental design problem.
5. You mentioned magnetic saturation as possible source, how could this explain the vibration?
6. In an attachment of the mentioned thread237-297373: Synchronous Motor Vibration - Approx 120 Hz w/ 1X sidebands: Synchronous Motor Vibration - Approx 120 Hz w/ 1X sidebands
it was mentioned that flat plates (inboard and outboard covers) are changed and affect the stiffness
1 - loose stator coils? I can't rule it out in theory but I think it's very low on the list. Loose stator coils (like any looseness) generate harmonics of an associated mechanical fundamental forcing frequency. In my case study linked above with steady torque, the forcing frequency acting on the coils was 2*LF (so we got 4*LF, 6*LF etc). In your case it could be coils responding to the varying component of the torque at 7.5hz. But there's nothing in the spectrum that narrows is to electrical cause and it could be many other things more likely/common than that. In particular simply coupling of the torque variation to radial movement via the machines asymmetric stiffness.
2 - external sources from grid. Very unlikely in my opinion… why would fundamental frequency 7.5hz be associated with the grid rather than the machine that operates at 7.5hz!
3 - bent shaft? Ordinarily would create 1x. Would only create harmonics in presence of some looseness or severe bearing problem. Seems unlikely to me although it never hurts to monitor what you can on the bearing (temperature, oil sample etc).
4 - Two machines with same behavior. You could interpret that as design problem as you suggest, or (my preference) you might interpret that as a sign that the response of the motor to this particular configuration (varying loading, mounting) is probably normal.
5 - saturation - saturation can increase CURRENT components on wye machine at frequencies of 5*LF, 7*LF, 11*LF, 13*LF. I can't say I've ever seen these show up in vibration or know exactly how they would influence vibration, but if they did see those frequencies (or double those frequencies), then I would consider saturation as a possible cause. I don't see anything like that in your vib spectrum.
6 - flat plates affecting response. Any flat plates attached affect the mechanical transfer function from forces to vibrations and in particular the resonances. You have already captured a bump test which is something like a transfer function in one of your attachments,
Again, bottom line it does not particularly alarm me as a symptom since the load torque is known to be rich in harmonics (and since torque is coupled to radial motion on horizontal machines with asymmetric radial stiffness).
The other question we might ask ourselves is whether these "known" load torque oscillations may be damaging to the motor. Certainly they may degrade coil tightness over time particularly if the winding was not well done to begin with. This might be something to factor into your long-term pm/inspection strategy, but nothing to worry about in diagnosing behavior that appeared immediately on new machines.
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(2B)+(2B)' ?