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Old Jun 3rd 2019, 03:37 PM   #1
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Precession effect on the top of a tower

Hello,

i have a problem that i need to solve, but i donīt know how, any help from anyone would be great

The problem is; in the top of a metallic tower is installed a radar antenna wich weights 170 kgs the hellix and about 230 kgs the motor.

The antenna is fixed to a metallic profile place in the geometric center of the tower, the antena and motor are excentric in the yy direction, the distance between the center of gravity of the tower and the center of rotation of the antenna is aprox 171.84 mm, and 5 mm in the xx direction.

The antenna rotates in the maximum at 60 rpm, about 2*pi rad/s.

Due to the excentricity i found a formula to calculate the FS, ( free force), wich is given by, FS=Mr x ω x e; eurocode 1 -parte 3, pag 39

MR- mass of the rotor
ω - angular velocity
e- excentricity

Iīm donīt know wich is the mass of the rotor is the mass of the antena + motor 400kgs?

In this case, because the antenna is excentric there is a precession movement. The angular moment of the antenna is constant given by I . ω;
the torque r x mg, the velocity of the movement is given by r x mg/I.ω rad/s.
If the angular velocity of the antenna diminush the angular velocity of precession incresses.

Is there any way, to calculate the magnitude of force of the precession induce in the tower?

Is the precession neglectable in this case( the antenna rotating induces considerable oscilation of the tower in the reallity)?
Wich equilibrium of forces is the more accurate, to quantify the forces induced by the antenna?

Thanks,
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Precession effect on the top of a tower-antenna-tower.jpg   Precession effect on the top of a tower-platform_at_45-m-high.jpg  
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Old Jun 5th 2019, 01:30 PM   #2
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I think the equation you are using for the force is incorrect - it should be:

F= m x w^2 x r

where m is the unbalanced mass and r is the radius of rotation of the unbalanced mass m. For reference, see https://en.wikipedia.org/wiki/Rotating_unbalance

This will give you the dynamic force due to the rotating unbalanced mass. This force excites the tower to vibrate. To determine the mode(s) of vibration and their magnitudes you will need to do a dynamic analysis of the tower, to determine its natural frequency of vibration, its stiffness, and its damping coefficient. This a detailed and complicated subject, these days typically done via computer simulation.
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Old Jun 13th 2019, 05:12 AM   #3
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precession on the top of the tower

Thank you, very much the formula was incorrect indeed.
In the case of the precession in the picture 1 i have the forces acting in a spining wheel with the axis horzintally.(see pictures)
If instead of the horizonatl axis , the axis is vertical and the spinnig wheel and axis is fixed in a rigid plate, where the is an excentricity between the centre of rotation and the center of gravity of the whole sistem . (see pictures)
there is a precession motion induced, what forces occur, in this way?

thank you
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Precession effect on the top of a tower-picture_horizontal-axis.gif   Precession effect on the top of a tower-picture_vertical-axis.gif  
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Old Jun 13th 2019, 07:39 AM   #4
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precession on the top of the tower

Concerning the unbalanced force, if the radar antenna is fixed to a 45 m, tower and. what is the value of the mass of the unbalanced force the mass of the tower + antena?
the excentricity is the distance between the centre of rotation of the antenna to the centre of garvity of the antenna +the tower?
is it correct to apply the unbalance force in the centre of gravity of the antenna + tower?

Thanks
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