Motor Inertia Simulation

[JohnComp]

I am trying to find an equation that simulates the inertia of a motor using on a brake dynomometer. Currently I have:

I=(Pm*RR*9549.3)/(RPM*a*g)

where:
I - Available inertia, kg-m-s^2
Pm - maximum motor power, typically 150% of rated power, kW
RR - I am unsure of what this truely is but my guess is Rolling Raduis of the wheel.
RPM - rotational speed of interest, rev/min
g - acceleration of gravity, 9.81 m/s^2
a - Vehicle acceleration, m/s^s

My calculations show that the units do not work out assuming that there are no units associated with "9549.3". I found this formula on a brake dynomometer testers and builders website called Link Testing.

If anybody has any ideas on the validity of this formula, or any other formulas that may be useful please let me know.

Thank you

 

[CJCPE]

The units work out. Power has the dimensions Watts or Newton-meters or kg-m^2/sec^2. The constant 9543.3 is 1000 x 60 / 2 x Pi to convert RPM to radians per second and kW to W.

 

[CJCPE]

Should have said Watts = Newton-meters/sec = kg-m^2/sec^3.

 

[JohnComp]

I do not see how the units work out.

((kg*m^2/s^2)*m*(rad/s))/((m/s^2)*(m/s^2)=kg*m*s not the units of inertia.

or bring the rad/s to the denominator instead of the numerator and you get - kg*m*s^3.

Maybe I am being ignorant but I do not see how the units work out.

 

[JohnComp]

Inertia is kg*m/s^2

 

[JohnComp]

okay
now that is correct

 

[CJCPE]

I had the inertia worked out to kg-m-s^2. Now that I have looked at it again, I think that it should work out to kg-m^2.

Does the equation we have been working on suit your problem if we get it right? Can you explain what data you are starting with and what you actually want to calculate?

 

[cswilson]

In any calculation like this, from a canned formula, you must be very careful about how the moment of inertia (MOI) is expressed. (By the way, because there is a lot of confusion when people are not explicitly clear about terminology, I prefer to use MOI for rotary systems rather than just "inertia".)

MOI can be expressed in units of mass*length^2. In SI units, this is kg-m^2.

MOI can also be expressed in units of force*length*time^2. In English units, you often see lb-ft-s^2. Since force is mass*accel = mass*length*time^-2, you see that the two methods of expressing MOI are equivalent.

It is critical to realize that while we use pounds and kilograms in common usage as interchangeable, in technical usage they are not. Kilograms are mass units, and pounds are force (weight) units. Where the confusion really comes in is when MOI is expressed in "hybrid" units, such as kg-m-s^2, as in this example. The intent is to use metric units in a form that is familiar to people who are more familiar with English units (or vice-versa).

IMHO, this typically creates far more problems than it solves. The "kg" in kg-m-s^2 is not a mass unit, but a force unit. It is the downward force exerted by a mass of one kilogram in normal earth gravity of 9.81 m/s^2. If you have to use these units, I believe you should label this "kgf" to make sure you distinguish it from the real mass units of "kgm". Remember that 1 kgf = 1 kgm * 9.81 m/s^2 = 9.8 N.

In your example, the factor of 1/g is in the equation to convert the force units to mass units.

Curt Wilson
Delta Tau Data Systems