To calculate the polar moment of inertia of a fan

In summary, the conversation discussed the representation of fan motors in a dynamic simulation of a power plant auxiliary system, specifically focusing on fan diameter, number of blades, and fan RPM. The fan blades were described as having a tapering cross section and varying mass-per-length from root to tip. The root and tip diameters of the fan disc were also given. The conversation then concluded with an estimation of the polar moment of inertia of the fan in Kg-m^2, which involved calculating the mass moment of inertia for the fan hub and one blade.
  • #1
siddarthan
1
0
1.The motors driving the fans of a large cooling tower must be represented in a dynamic
simulation of a power plant auxiliary system.
Each fan can be described as follows:
Fan diameter = 4.5 meter
No of blades/fan = 6
Fan RPM = 90
The fan blades have a tapering cross section.
The fan cross section may be taken to taper linearly from root to tip.
The mass-per-length of each blade may be taken to vary from 8 Kg/m at the root to 3Kg/m
at the tip.
The root diameter of the fan disc is 1m.
The tip diameter of the fan disc is 4.5m.
Estimate the polar moment of inertia of the fan in Kg-m^2

2. unable to figure out

3. unable to figure out
 
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  • #2
This is not a hard problem; it simply has several parts to be worked out.

First, the fan hub is a disk, so look up the formula for the mass moment of inertia (MMOI) for a disk and apply the given data for the fan hub to geet that part.

Secondly, you are told how the mass per length varies, and you know both the rood radius and the tip radius, so you can perform the following integral for one blade:

MMOIblade = ∫r1r2 r2 (mass/length) dr

Use these two results, with appropriate multipliers, to build the required final result.
 

FAQ: To calculate the polar moment of inertia of a fan

What is the polar moment of inertia?

The polar moment of inertia is a measure of an object's resistance to rotational movement around its central axis. It is a combination of the object's mass and its distribution relative to the axis of rotation.

Why is it important to calculate the polar moment of inertia for a fan?

Knowing the polar moment of inertia for a fan is important because it allows us to understand how the fan will behave when subjected to rotational forces. This is especially important for fans used in machinery or vehicles where precise movement and control are necessary.

How do you calculate the polar moment of inertia for a fan?

The polar moment of inertia for a fan can be calculated by summing the moments of inertia of each individual component of the fan, such as the blades and the hub. This can be done using mathematical formulas or through computer simulations.

What factors affect the polar moment of inertia of a fan?

The polar moment of inertia of a fan is affected by several factors, including the shape and size of the fan, the distribution of mass within the fan, and the speed at which it rotates. The material and density of the fan's components can also impact its polar moment of inertia.

How can the polar moment of inertia of a fan be optimized?

To optimize the polar moment of inertia of a fan, engineers can make design changes to the fan's components, such as using lighter materials or altering the shape and distribution of mass. Computer simulations can also be used to test and refine different designs to achieve the desired polar moment of inertia.

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