# How to measure the moment of inertia of a motor's rotor?

Hello, I need to measure the moment of inertia of a DC motor's rotor. Any suggestion? Thanks

## Answers and Replies

What kind of relevant measurement tools do you have access to? Do you have a motoring dyno?

There is always this concept available as well

What kind of relevant measurement tools do you have access to? Do you have a motoring dyno?

There is always this concept available as well

Thanks. I don't have a motoring dyno. I am trying to measure the inertia at home without fancy equipment.

The only method I know of is described in Fig. 2.10.5 on 2-73.
https://www.elsevier.com/books/dc-motors-speed-controls-servo-systems/zhou/978-0-08-021714-7

Anybody knows what Collet is? Is it part of the rotor? From the description, it seems to be removable so that one could connect it to a rotor or a dummy to measure the spinning period. I cannot find a removable part from the rotor.

https://bbqbbq2bbq.smugmug.com/My-First-Gallery/i-fpFQz8H/A

• RogueOne
berkeman
Mentor
Thanks. I don't have a motoring dyno. I am trying to measure the inertia at home without fancy equipment.
I would be inclined to just use a string and a weight. Wrap the string around the shaft some number of times and use a stopwatch to measure how long it takes for the weight to fall through some distance. Use the diameter of the shaft and the mass of the weight in your calculations to get to the MOI. Sounds like a fun project... I would be inclined to just use a string and a weight. Wrap the string around the shaft some number of times and use a stopwatch to measure how long it takes for the weight to fall through some distance. Use the diameter of the shaft and the mass of the weight in your calculations to get to the MOI. Sounds like a fun project... "to fall through some distance"? I think the book mentioned about spinning.

What should I do in regard to the "Collet"? I don't have it but the equation requires the MOI of the collet.

Tom.G
Science Advisor
Anybody knows what Collet is?
Similiar to the Chuck on an electric drill; usually does not require a key to tighten.

There is a way you can measure MMoI of irregular geometry by attaching it to a spring (say a steel rod) about its centre and then measuring the period. From that you can find the Inertia using fundamental vibration analysis.

fN = 1/T = 1/(2*pi)* sqrt(k_theta/I)

Natural frequency or period, T, can be measured. K_theta of the steel connecting rod is GJ/L. Substitute into equation above and you will get an approximation of the Inertia.

Last edited:
• berkeman and Randy Beikmann
Randy Beikmann
Gold Member
There is a way you can measure MMoI of irregular geometry by attaching it to a spring (say a steel rod) about its centre and then measuring the period. From that you can find the Inertia using fundamental vibration analysis.

fN = 1/T = 1/(2*pi)* sqrt(k_theta/I)

Natural frequency or period, T, can be measured. K_theta of the steel connecting rod is GJ/L. Substitute into equation above and you will get an approximation of the Inertia.

I agree with Sirsh. Natural frequencies are little affected by typical amounts of friction, yielding smaller errors than measuring a steady acceleration.

I actually had to do this years ago. I hung a mass m from the rotor shaft by a light but stiff rod at distance L, making a physical pendulum. After deriving the equation for the natural frequency, then measuring it, I was able to back-calculate the unknown rotor inertia J.

There is a way you can measure MMoI of irregular geometry by attaching it to a spring (say a steel rod) about its centre and then measuring the period. From that you can find the Inertia using fundamental vibration analysis.

fN = 1/T = 1/(2*pi)* sqrt(k_theta/I)

Natural frequency or period, T, can be measured. K_theta of the steel connecting rod is GJ/L. Substitute into equation above and you will get an approximation of the Inertia.

Thanks. What is l, GJ and L? How do I find those values?

Thanks. What is l, GJ and L? How do I find those values?

I is the Inertia of the object in question i.e. Motor rotor. G is the shear modulus of the spring material, J is the polar moment of the spring - if it's a circular cross-section this would be (pi/32)*d^4, and L is the length of the spring.