Calculate the forces acting on the Driven pulley (Centrifugal fan)

[SikandarAfzal63]

TL;DR Summary

Hi all,
I have a centrifugal fan that is driven by a belt and pulley system via an electric motor. I want to calculate the forces acting of the driven pulley?

The main aim of doing this is, i want to perform modal analysis on the shaft of the fan, and i want to also include the resultant force and the moment acting on the shaft of the fan due to the motion on the pulley. I will attach the formulas that i found and also system image. Can you guys please let me know if i am proceeding in the right way.

 

[jrmichler]

The radial force on the shaft is the total belt tension. When the motor is running, the decrease in tension on the slack side is equal to the increase in tension on the tight side, so the total radial force is constant.

The fan drive torque can be calculated from the actual fan power and RPM. The fan RPM is found from the motor RPM and pulley ratio. The actual fan power is found from the fan curve, which is available from the fan manufacturer. The fan shaft torque is then calculated from the fan power and RPM.

Note that none of this should have a measurable effect on the modal frequencies, which are determined by the mass and stiffness of the shaft, bearings, fan, pulley, and housing.

And welcome to PF.

 

[SongDog]

How thorough do you wish to be?

If you seek to predict the acoustics you will need to look at the air plenum as a damped resonant dynamic system, driven by an impeller that has angular momentum, elastically coupled to a motor and idler that also have angular momentum. The design of the impeller, particularly the number of blades, changes the acoustic forcing frequency and waveform as functions of the impeller rotation frequency. Keeping that forcing frequency far from the duct resonant frequency quiets the duct. Meanwhile, dynamic back pressure on the impeller will, to some limited extent, modulate the impeller frequency

If you want to run intermittently or at variable speeds then startup and shutdown transients matter: you will want to consider how this impacts your non-slip constraint. Even at steady state, there will be elastic cycling of the belt tension at the blade and impeller frequencies, so depending on the belt construction it will fatigue over time, changing its behaviour. What design life are you choosing?

Each component part has production tolerance on its parameters. A robust system design considers what the worst-case combination of these tolerances does to the system behaviour.

Of course you can make simplifying assumptions, but you should recognize that you are doing so and test their validity.

 

[SikandarAfzal63]

The radial force on the shaft is the total belt tension. When the motor is running, the decrease in tension on the slack side is equal to the increase in tension on the tight side, so the total radial force is constant.

The fan drive torque can be calculated from the actual fan power and RPM. The fan RPM is found from the motor RPM and pulley ratio. The actual fan power is found from the fan curve, which is available from the fan manufacturer. The fan shaft torque is then calculated from the fan power and RPM.

Note that none of this should have a measurable effect on the modal frequencies, which are determined by the mass and stiffness of the shaft, bearings, fan, pulley, and housing.

And welcome to PF.

Thank you so much @jrmichler for the reply.

I totally understand your point of view as in the mass and stiffness matrices we have terms related to kinetic and potential energy. But my point to ask above thing was to find the magnitude and direction of the force for the belt and pulley system on the shaft and also on the bearing, so that i can make more precise deduction for the shaft deflection.
As this force is a vector and it will change its direction continuously, so should i take this vertically downward, when maximum force acts on the bearing (which includes mass of the shaft, impeller).
Because i have a fog in my mind regarding the fact that, slack side the force/tension is less and the tight side has more tension/force so the resultant force will act in what direction?

 

[tech99]

A propos #2, I think the radial force on the shaft is twice the tension in the belt.

 

[jrmichler]

Because i have a fog in my mind regarding the fact that, slack side the force/tension is less and the tight side has more tension/force so the resultant force will act in what direction?

The answer is in a free body diagram (FBD) (search the term) as shown below. The belt tension is $T_1$ on one side and $T_2$ on the other side. The resultant force on the shaft is $F_R$. The torque on the shaft is $T$.

The resultant force $F_R$ is equal and opposite to the total tension of the two sides of the belt. This is true whether the forces $T_1$ and $T_2$ are equal or not equal. If the forces $T_1$ and $T_2$ are not equal, there is a torque $T$. In all cases, both the forces and moments (torques) through the center of the pulley sum to zero.

In the case shown, the belt tensions are vertical. In that case, the resultant force is also vertical. This is true whether $T_1$ is equal, or not equal, to $T_2$. If the force $T_1$ is equal to $T_2$, the torque $T$ is zero. If the motor is driving the fan, $T_1$ is not equal to $T_2$, and there is a torque $T$.

The total force on the shaft is $F_R$. That is the force used to calculate the bearing loads and bending stress in the shaft. The torque on the shaft is $T$. The torque is used to calculate the torsional stress in the shaft.