# Precession effect on the top of a tower

#### Luislb

Hello,

i have a problem that i need to solve, but i don´t 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

I´m don´t 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,

#### Attachments

• 22 KB Views: 3
• 25.3 KB Views: 3

#### ChipB

PHF Helper
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.

#### Luislb

Thank you soo much, for your concern, it´s very important to me discuss the subject with someone who know!

You´re absolutelly right the correct formula of force is F= m x w^2 x r, like i said before it´s in the eurocode.

Although the r is the excentricity between the centre of roation, and the center of mass.

My question is the following: beeing the rotating antenna (radar antenna) fixed in the top of the tower to a profile, and the radar antena + the motor already the excentric, what is the unbalance mass that i should considerate to calculate the unbalanced force? the mas of the antenna +motor and it´s excentricity; the mass of the antenna +motor + profile and it´s excentricity, or the mass of the antenna + motor + profile (suport) + mass of the tower?

i´m have done a dinamyc simulation in a software, but i need to undersant if i´m inputing the right forces, the tower as the first mode of vibration is about 1.63 Hz, yhe dumping i´m using is 2.0%, it´s a metallic tower made by mettalic angles.
Do you think it´s correct to consider, in the dinamic analysis of the tower, in the harmoic movement and consider the angular velocity of the antenna 2*pi rad/s?

In the case of the precession induced by the rotation of the antenna, and because of the excentricity between the center of rotation of the antena and the center of gravity of the tower, how can i quantify the forces, that are induced by the antenna in the tower?
In your oppinion this forces induced in the tower are neglectable?

in the case of a horizontal gyroscope spinning to a certain angular velocity, and suported horizontaly it does´t fall, and turns aroud in one direction, or anther depending of the direction of the rotation of the disc and the torque, because of the distance r ( between the centre of rotation of precession, and the center of gravity of the gyroscope) given by rx mg, the angular moment L, is given by I x W, so the precession is the L "chasing" the torque, you think i can reproduce this magnitudes in the tower?

I know that in this type of towers when the antenna rotates, there´s big oscilation of the tower, i need to understand why, because this problem is one of my concers in my last work thesis, to finish my master in civil engeneering.

thank you very much!

#### Luislb

Thank You chipB,

you´re right that´s the correct formula, to calculate the force what is the unbalanced mass, and the correct r ( in this case is the excentricity between the centre of rotation and the centre of gravity)?

the mass of the antenna+motor? and the excentricity between the centre of rotation and the centre of gravity of the antenna+motor? ( in this case the force is minimum)
the mass of the antena +motor + tower and the excentricity between the centre of rotation and the centre of gravity of the antenna+motor+tower?

I´ve preformed a dinamic analisys in a software, that simulates an harmonic motion, the fisrt mode of the tower is about 1.63 hz, and i´m assuming a damping of 2% ( metallic tower).In this case what is the correct angular velocity of the exciting dinamic free force? is it correct consider the angular velocity of the antenna 2*pi rad/s?

In terms of precession induced by the rotation of the antenna in the tower ( because the antenna is fixed in the tower and there is an excentricity between the centre of rotation of the antenna and the centre of gravity of the antenna + motor + tower), how do i calculate the magnitude of the precession of the antenna induced in the tower?

thanks,

Luis

#### Luislb

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

#### Attachments

• 34.2 KB Views: 0
• 270 KB Views: 0

#### Luislb

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