Counter-rotating mass to counteract inertial spin

[scottthomascarter]

How do I determine the required combination of spin rate and disc mass to counteract the inertia of a second spinning disc? I have complete knowledge of and control over both disc masses and spin rate and geometry. Let's say Disc A geometry, mass and spin rate are fixed and constant, so I can determine the moment of inertia. The objective is to use Motor B spinning Disc B to counter-rotate and cancel the inertia of Motor A spinning Disc A, the result being that the "floating" frame remains motionless, spinning in neither direction. This is an idealized experimental set-up, but the principle will be applied to a flying vehicle (similar to a dual counter rotating bladed helicopter). My hesitant assumption would be that the same exact disc at the same spin rate would do the job, but the objective is to reduce the Disc B mass and compensate by increasing the spin rate or altering the moment of inertia (via geometry). Thanks very much for helping if possible.

 

[Dr.D]

Have you drawn the relevant free body diagrams? That's where you need to start.

 

[berkeman]

the objective is to reduce the Disc B mass and compensate by increasing the spin rate or altering the moment of inertia (via geometry).

You may already be doing this, but be sure to include the motor's moment of inertia along with the disc.

 

[scottthomascarter]

I've schematically laid it out (accompanying mock up). I'm looking for some guidance on the controlling equations and principles to make the (relatively simple I think) calculations. A free body diagram would just be a 2D version of this with the variables labeled. But the missing piece of my puzzle is what I then do with those variables. I think the short list of variables are mass of the disc, rotational speed or angular velocity, and maybe 2nd moment of area of the disc, as the distribution of the mass of the disc is not required to be uniform through the entire radius of the disc. I know these three for each disc, but what to then do with them?

 

[scottthomascarter]

You may already be doing this, but be sure to include the motor's moment of inertia along with the disc

Good point, the armature of the motor will be spinning even though the body is not. That essentially adds to the moment induced by the entire assembly. I'll dissect a motor to get that internal geometry and make my best estimate on it.

 

[berkeman]

I'll dissect a motor to get that internal geometry and make my best estimate on it.

It looks like you are using the same type of motor for each one, so you might just be able to determine it experimentally by finding the spin rate needed for one motor without a disc to balance the other motor with a disc with a known MOI...

 

[scottthomascarter]

In my simplified example (our functional mock up) the motors are the same, and experimental results will be had. But the real result we will be going for will be in a flying vehicle with a spinning impeller for downward thrust, and we will be counteracting that rotational force using a counter-rotating mass of a very different geometry (so a different MOI). Which is why I'm after the governing principles/equations so we can design our impeller and disc accordingly. I'll definitely get some good data and empirical evidence from the mock up, but then we'll need to apply that to the vehicle, and some numbers would be a good thing to have in hand.

 

[berkeman]

But the real result we will be going for will be in a flying vehicle with a spinning impeller for downward thrust, and we will be counteracting that rotational force using a counter-rotating mass of a very different geometry (so a different MOI).

If I understand what you are saying, I don't think it will work. The rotating propeller/impeller is using torque to accelerate the air mass downward to generate lift, and you can't counter that constant torque with just a counter-rotating disc. You would need to continually be accelerating that disc to be getting a counter-torque, and that's only going to work for a few seconds at best.

 

[sophiecentaur]

If only for interest, you could look at Reaction Wheels - very commonly used to stabilise the attitude of spacecraft .

 

[scottthomascarter]

If I understand what you are saying, I don't think it will work. The rotating propeller/impeller is using torque to accelerate the air mass downward to generate lift, and you can't counter that constant torque with just a counter-rotating disc. You would need to continually be accelerating that disc to be getting a counter-torque, and that's only going to work for a few seconds at best.

The flight control computer achieves that at millisecond intervals using on board accelerometers and gyros. DC brushless motors (the kind used in most drones currently) respond equally efficiently (i.e. almost instantaneously) to Electronic Speed Controller inputs based on sensor feedback. But that's not the issue, the principle is sound. I just need to quantify that principle to predict how much energy needs to be planned for. I know it's not as simple as massA x angular velocityA = massB x angular velocityB if those masses are different "shapes". That's where the factor of the second moment of area comes in (I think). I just don't know how, and that's what I'm looking for.

 

[berkeman]

(the kind used in most drones currently)

Drones use counter-rotating props to avoid yaw issues.

I think you missed my point. If you have one vertical rotor to provide lift for an aircraft, you cannot counter the torque by just spinning an on-board disc. The lifting propeller is interacting with the outside world (via the air that is flowing down through it), and the internal disc is not. It almost sounds like you are thinking there is something magical that you can do on-board the single-rotor aircraft to keep it from going into a continuous yawing spin...