Understanding Unbalance Force in Rotating Systems

1 reply · 2K views · last reply
synMehdi
Messages
38
Reaction score
0
TL;DR
understanding what happens to a rotor when an unbalance mass is added in a spring model bearing
I would like to undertand more the force caused by unbalance in a rotor, assume that the bearing is represented with 2 springs like above:
Diagram of a rotor inside a stator ring, with the rotor centre O labelled O=O'=Cg, two zigzag springs connecting the rotor to the stator at points E/F and H/D, and dashed diagonal construction lines.

The geometrical center of the rotor ##O## is equivalent to it center of gravity ##C_g## and the center of the stator (bearing) ##O'##
The rotor is perfectly balanced all the centers coincide

When the rotor has an unbalance mass ##M_u##, the 3 centers no longer coincide:

Schematic cross-section of a rotor inside a circular stator: outer stator circle, inner rotor circle labelled Mr, centres O, O' and Cg, eccentricity e, unbalance mass Mu with force Fu and bearing force Fb indicated.

I ommited the springs representing the bearing. The rotor (with mass ##M_r##) turns and orbits around the center of the stator ##O'##
The unbalance force is defined as ##F_u=M_u\cdot r\cdot \omega^2 ##
My question is: What is ##r## ? Is it ##O'M_u## or ##OM_u##.
I understand that these two vectors are virtually the same in an up-to-scale rotor
The unbalance can also be defined as ##F_u=(M_r+M_u)\cdot e\cdot \omega^2 \approx M_r\cdot e\cdot \omega^2##
so my second question is: How about ##e##?. Is it ##O'Cg## or ##OCg## ?
This time the two vectors are not virtually the same

I guess I want to understand what's going on when the rotor is orbiting and turning around itself. My guess is ##e=O'C_g## because ##O'## will depend on the stiffness of the bearing. Infinite stiffness will make ##O'=O## and the unbalance force will be described with no problems. zero stifness will make ##O'=Cg## and zero unbalance force, right? It should seem ##e## should be ##O'Cg## but I don't fully understand why.
 
Your post is not drawing any answers, and I think the reason is because of the fuzzy way it is stated. I'd suggest that you start again, include the mathematics of your understanding, and ask specific, answerable questions. Things like "I guess want to understand what's going on ..." really is asking someone to pour knowledge and understanding into your mind, something way beyond our capabilities.
 
  • Like
Likes   Reactions: BvU