Forced Torsional Vibration

[mechanicaljw]

Hello All,

I have done free torsional analysis that i now want to extend to the case when there is some forcing. Our electric motor is driving the compressor and this is exciting the compressor at its first mode. I have now been able to get a time series data of the motor torque that is of the form T(t)=asin(omega*t+beta)+T0, where a is the excitation amplitude, T0 the steady torque, and beta the phase shift determined by curve fitting the experimental time series data of the torque. In the book Mechanical Vibrations by G. K. Grover (Page 338) an example was considered that assumes the forcing torque to be of the form T=T0sin(omega*t). My question is in case the forcing is like the one i determined from curve fitting, how do i account for the phase shift beta? And also the T0? I am thinking that T0 should not play any role in the forcing??

Any suggestion on how to handle this would be appreciated. A citation that considers such a case will also be appreciated.

Thanks!
Jimmy

 

[electricpete]

In the book Mechanical Vibrations by G. K. Grover (Page 338) an example was considered that assumes the forcing torque to be of the form T=T0sin(omega*t). My question is in case the forcing is like the one i determined from curve fitting, how do i account for the phase shift beta?

Unless you are comparing two signals or t=0 has some special definition, beta is irrelevant. Sorry if I have misunderstood.

And also the T0? I am thinking that T0 should not play any role in the forcing??

For a linear system, dc force T0 would only cause dc response, not torsional oscillation. Your system may or may not be linear.

I have done free torsional analysis that i now want to extend to the case when there is some forcing. Our electric motor is driving the compressor and this is exciting the compressor at its first mode.
I have now been able to get a time series data of the motor torque that is of the form T(t)=asin(omega*t+beta)+T0, where a is the excitation amplitude, T0 the steady torque, and beta the phase shift determined by curve fitting the experimental time series data of the torque.

Are you working with measurements or a model?
What makes you think motor is exciting a torsional mode (rather than compressor)? What is the frequency of the torsional vib? Is this motor driven from vfd?


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(2B)+(2B)' ?

 

[mechanicaljw]

Hello electricpete,

I am developing torsional models and for the forcing or external torque we measured time series data of the torque and use curve fitting to get the forcing function.
The electric motor is running with a VFD:

The first mode frequency is the torsional frequency. The crtical speed at which this is happening is 1300 rpm and for all the test we are having torque peak at 21.7 Hz.

When we run the compressor using a hydraulic drive there was no resonance or torque peak from our pulse run up torque measurement data. Also, we braced the compressor to the flow and repeated another test and got torque peak at the same frequency. By bracing the compressor we changed the structural stiffness and if the resoance was structural we expected to see a change in the behavior of the machine.

I hope this answers your questions?

Thanks!
Jimmy

 

[Tmoose]

Hi Jimmy,

What is the compressor type? Is the calculated resonance also ~ 21.7 Hz ?

 

[electricpete]

You have a peak at 21.7hz when the machine is running 1300 = 21.7hz driven by electric motor.
You have a no peak near 21.7hz when the machine is running 1300 = 21.7hz driven by hydraulic motor.

What does it prove? Well we know for a fact any torsional resonant frequency changed when you changed the system to remove the motor. It doesn’t seem to prove much.

I’d think compressor is most likely cause of any torque oscillations at one times running speed (assuming no belt or gearbox) because it is inherent in the nature of reciprocating (assumption) compressors to cause torque oscillations which are at running speed (or harmonics or subharmonics…).


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(2B)+(2B)' ?

 

[electricpete]

Another possibility (probably less likely*) is that you have a rotor lateral critical speed at 1300rpm and the associated modeshape is one of a flexible rotor with very little movement at the bearings. At that frequency, the rotor acts very flexible and bearings act comparatively stiff almost like a rigid support. The resonant frequency depends primarily on the rotor and not very much on changes to bearings or any changes by stiffening the structure. *I’m inclined to think very few rotors would be flexible at such a low frequency, but you never know…

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(2B)+(2B)' ?

 

[mechanicaljw]

@Tmoose-The compressor is a screw compressor (with male and female rotors and drive through female rotor) that we run between 1000 to 1800 rpm. The critical element in the system has also be shown to be the connection between the drive (in this case the electric motor) and the compressor. Looking at the mode shapes, one can argue that that the entire compressor is behaving like a rigid body as the relative angular deformation within the compressor is about uniform. The largest angular deformation we are getting is always between the nodes connecting the electric motor to the first stage gears of the compressor.

Also, by tunning the input shaft to a certain torsional stiffness we were able to avoid this resonance. The problem is that the shaft in question is not standard and so we therefore cannot use it in serial production.

Thanks to all for your input but i wanted help on how i could incorporate this forcing function into my torsional model as described in my original post.

Jimmy

 

[electricpete]

It's still not clear what you are trying to do.

I have now been able to get a time series data of the motor torque that is of the form T(t)=asin(omega*t+beta)+T0, where a is the excitation amplitude, T0 the steady torque, and beta the phase shift determined by curve fitting the experimental time series data of the torque.

How was this torque data obtained? Experimental measurement? ... of what? (electrical or mechanical)?
I assume asin is a typo?
What does this beta mean to you? It implies to me only phase relative to t=0, which seems arbitrary.

In the book Mechanical Vibrations by G. K. Grover (Page 338) an example was considered that assumes the forcing torque to be of the form T=T0sin(omega*t). My question is in case the forcing is like the one i determined from curve fitting, how do i account for the phase shift beta?

You tell us - what does your beta represent?

And also the T0? I am thinking that T0 should not play any role in the forcing??

I agree, under ASSUMPTION of linearity, the static term T0 plays no role in the dynamic response.

Our electric motor is driving the compressor and this is exciting the compressor at its first mode

You did not respond to previous comments indicating your logic to identify motor as cause seemed incorrect.



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(2B)+(2B)' ?

 

[Tmoose]

What type of coupling is being used?

Screw compressors generally have significant pressure variations internally and at their discharge, and the magnitude varies with load.
Figures 10, 11, and 12 here -

http://docs.lib.purdue.edu/cgi/viewcontent.cgi?article=1725&context=icec

I'd expect the input shaft torque to vary with the pressure magnitude. The frequency of the pulsation would depend on compressor configuration.

If "The largest angular deformation we are getting is always between the nodes connecting the electric motor to the first stage gears of the compressor" it sounds like the coupling torsionial stiffness is low compared to the shafts, creating essentially a 2 mass system, and could be varied to de-tune the resonance like you did modifying shaft stiffness.

Although there is always some cross effect between supports and rotating machine elements, I think the torsional mass-spring-mass system of the motor-coupling-compressor might not rely much on support stiffness.