Determine bending moment from acceleration measurements
Determine bending moment from acceleration measurements
(OP)
I am trying to determine bending moments from acceleration measurements. I can integrate the acceleration signal twice to get deflection, but then am unsure how to obtain the bending moment from that deflection data.
Deflection theory works from the bending moment to get the deflection but I am trying to get the bending moment from the deflection.
Any assistance would be appreciated.
Deflection theory works from the bending moment to get the deflection but I am trying to get the bending moment from the deflection.
Any assistance would be appreciated.





RE: Determine bending moment from acceleration measurements
The simplistic approach. Assume that an unknown force F or a moment M is applied to the shaft at some location based on your knowledge of the system and your suspicion of the vibration cause. Use that force or moment to determine a deflection shape to within a scalar constant. Use measured amplitude to determine the scalar constant. Moment is E*I*dy^2/dx^2.
Now the caveats.
First – you are measuring acceleration I am guessing it is on bearing housing. Relationship between bearing housing displacement and shaft displacement is unknown.
Second – is it really fair to model the vibration as originating with a force or moment at one location. Forcing functions such as misalignment are much more complicated.
I'm sure there are more caveats, but those two come to mind.
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RE: Determine bending moment from acceleration measurements
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Eng-tips forums: The best place on the web for engineering discussions.
RE: Determine bending moment from acceleration measurements
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Eng-tips forums: The best place on the web for engineering discussions.
RE: Determine bending moment from acceleration measurements
From 3 adjacent deflections work out the radius of curvature of the beam (schoolboy geometry)
Then
M/I=E/R
I bet you thought it was harder than that!
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: Determine bending moment from acceleration measurements
I would think in that case the bending stresses you calculate will represent a minimum value.... the actual are unknown and can be much higher than calculated and you have no way to bound them without a better model.
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RE: Determine bending moment from acceleration measurements
This M/I=E/R=s/y is the fundamental beam equation, everything else is derived from it (for elastic beam theory).
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: Determine bending moment from acceleration measurements
=====================================
Eng-tips forums: The best place on the web for engineering discussions.
RE: Determine bending moment from acceleration measurements
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: Determine bending moment from acceleration measurements
=====================================
Eng-tips forums: The best place on the web for engineering discussions.
RE: Determine bending moment from acceleration measurements
=====================================
Eng-tips forums: The best place on the web for engineering discussions.
RE: Determine bending moment from acceleration measurements
Could that not be misleading, such a signal could indicate oscillation without any applied moment. And any static moment would not be picked up.
Why not perform a dynamic characterization.
Fe
RE: Determine bending moment from acceleration measurements
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: Determine bending moment from acceleration measurements
That only works if you have a constant moment going through the beam. If this is a cantilever beam, he needs to work out the bending using McCauley's method or by looking it up in a handbook. Going from deflection to moment is then fairly easy.
RE: Determine bending moment from acceleration measurements
M = E*I*dy^2/dx^2
SigmaBendingMax = c*M / I where c is distance neutral axis to extreme fiber
It doesn't matter what applied or reaction forces or moments created the bending, we can solve that maximum bending stress from the deflection shape. (Assume shear stress is negligible... beam is generally long and thin etc).
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RE: Determine bending moment from acceleration measurements
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