(WK^2) Weight Moment of Inertia?

[ttaylorcad]

Trying to figure out the minimum HP required to accelerate a fan (blower) wheel. Nema publishes the Load Wk^2 values for motors at different RPM/HP. I have modelled the fan wheels in cad and have the inertial properties ie. mass moment of inertia in the axis of rotation (Iz). Is this the same? Thanks

 

[EngJW]

Moment of inertia terms are confusing because I and J are sometimes used interchangeably. Generally J is a mass moment of inertia about an axis but I is sometimes used for the same thing. J is also an area moment for torsional stress calculations and I is also an area moment for bending stress.

As far as polar moments of inertia such as wr^2 and Iz, wr^2 does not include the g term so its units are pounds and inches. Iz should have the g term (it is based on mass instead of weight) so it will have sec^2 in the units. The only way to tell for sure is to look at the units. For acceleration calculations you need a moment of inertia that includes the g term.

Hope all this mumbo-jumbo makes sense.

 

[ttaylorcad]

Thanks for the response, this was my line of thinking as well. What was confusing for me is that my cad software (Inventor) is giving me the Inertial properties in lbmass in^2 units. I had never really heard of or used "weight moment of inertia" before so I wanted to make sure that my I3/Izz was the Wk^2 or WR^2 that I needed.

 

[gwolf]

ttaylorcad - try SI units and you will avoid this sort of confusion for ever.

Don't forget the aerodynamic drag if you connect the wheel to anything with wind resistance, it will become far more dominant than inertia as the speed increases.

 

[stanier]

Beware some motor manufacturers , especially from Europe, use the term GD^2. This is based upon diamter and not radius hence the term is a factor of four higher.

 

[svanels]

The unit in SI terms for moment of Inertia is:
kg m²
which would have the equivalent lbmass in² in imperial units

For a cilinder
I = 1/2 M r² or I = 1/8 M d²
where M = mass, r = radius and d = diameter

Oke things complicate when you have cavities like in impellers etc. These can be considered as composite entities with the cavities having negative mass. The total I is obtained summing all these positive and negative inertias.

It is obvious that when at the end you get a negative number, there is something wrong with your calculator

The Wk² or Mk² is used to compare an 8" fan with a mass M with an equivalent solid cylinder with mass M and equivalent radius k, which in this case will be much smaller then 8"