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Need Help Related to Rotational Inertia

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Patrick

Thu Feb 14 2013, 04:12AM

Registered Member #2431 Joined: Tue Oct 13 2009, 09:47PM
Location: Chico, CA. USA
Posts: 5639

Hey all,

Its me again, im pondering and reading everything i can find on rotational inertia. im trying to increase the mass of a rotating body.

ok, so i need more control authority available to the flight controller and human pilot. So far ive had tail-stalls where the tail crashes first into the ground. i relaize that adding a small mass to the tips of the tri-prop would increase (greatly) the inertia, and that at the same speed the same mass added atnear the center has much less inertia.

so with that in mind my specific question is: how can i calculate a increase in inertia, ie lets say i want to increase inertia by 10%, how much mass must be added at the inner diameter (1.6 inches) of the motor bell.

now for numbers and facts...
--prop: tri-blade 10 inches in dia, 26 grams. [10x7]
--motor bell: metal, 1.6 inches dia. wheighs 36 grams.
--At hover: 6000-ish rpm, on each rotor.
--total rotating mass is 62 grams times two rotors.

let me post pics too...

The prop and motor seen above.

Stator. 15v, 12,000rpm capable @ 1kg of lift

All flight testing has been done with what you see here. 62 grams of rotating aluminum, magnets, and plastic...

Prop and rotor hub, mass of solder too, 68 grams seems possible.

increasing the mass by wraping solder around the motor bell. (just a crazy thought)

throttle for sustained hover is approximately 6000 rpm, as can be seen it oscillates between 5800 and 6200rpm...

data logging, impossible to make progress with out it!

Ash Small

Thu Feb 14 2013, 04:30AM

Registered Member #3414 Joined: Sun Nov 14 2010, 05:05PM
Location: UK
Posts: 4245

Hi Patrick, I'm not quite sure what your question is

but I'd suggest placing the 'mass' at the extremities of the prop. This can be accomplished using a circular 'section' (ie part of a cylinder) attached to the outer edge of the prop.

Hopefully this suggestion will give you something to 'ponder'

(EDIT: Would this be to aid/increase stability, by any chance?)

Edit: This was posted before Patrick finished/edited his OP above.

Sulaiman

Thu Feb 14 2013, 06:05AM

Registered Member #162 Joined: Mon Feb 13 2006, 10:25AM
Location: United Kingdom
Posts: 3140

Rotational inertia is the sum of all (mass x radius.squared)
so tripling the distance of mass from the center
increases rotational inertia by nine times etc.

So Ash's suggestion offers the greatest increase in rotational inertia for the least increase in mass.

Patrick

Thu Feb 14 2013, 06:11AM

Registered Member #2431 Joined: Tue Oct 13 2009, 09:47PM
Location: Chico, CA. USA
Posts: 5639

Sulaiman wrote ...

Rotational inertia is the sum of all (mass x radius.squared)
so tripling the distance of mass from the center
increases rotational inertia by nine times etc.

So Ash's suggestion offers the greatest increase in rotational inertia for the least increase in mass.

yes im fully aware of this, as it is with the heavy rim on flywheels, for ripple smoothing on engines... but with a prop i have aerodynamic constraints, the last 50% of radius is responsible for 80% of the thrust generated, and the tips are weakest mechanically... so i must consider those factors as well.

from the first pics and post, im thinking of wraping solder around the motor bell (0.8 inch radius), to increase the inertia 10% over the current inertia. even though the inner radius is less desirable (needing more mass)...

and yes Ash, its meant to increase the force the flight controller can rely on, hopefully solving my "tail-stall" problem...

(EDIT: or better yet a thin rectangular copper or brass strip, that can be coiled up along the circumference of the motor bell, and epoxied in place.)

else, as Ash and Sulaiman have said, ill have to add a tiny mass to all 3 tips, hopefully not cuasing aerodynamic flutter or mechanical disintegration. Remember, props are highly engineered structures id rather not sabotage by mucking around with if i can avoid it.

EDIT: im thinking about what Sulaiman has said, in fact that "radius squared" bit is inspiring, what if i put very thin copper foil on the upper surface of the prop tip? 0.5 x 0.75 inches and 0.010 thick, and it could be made to conform to the curve of the airfoil, held in place with epoxy or pmma. i worry about flinging bits of metal at high speed at people though if they break loose...

Dr. Slack

Thu Feb 14 2013, 08:18AM

Registered Member #72 Joined: Thu Feb 09 2006, 08:29AM
Location: UK St. Albans
Posts: 1659

Props have an rpm limit based, along with other things like flutter stability, on their strength. If you add mass to the tip, it would be a very good idea to re-qualify the rpm you can drive it to. It's a shame that the best place to add mass to if you want the best increase in inertia for the least increase in total mass is the worst place mechanically for prop integrity.

Have you considered modifying the time constants in the controller so it *looks* like the motor+prop has more inertia. That will weigh nothing, leave the prop full strength, and allow you to tune the extra inertia quickly. That's if you have access to the appropriate node to add the function.

Patrick

Thu Feb 14 2013, 08:25AM

Registered Member #2431 Joined: Tue Oct 13 2009, 09:47PM
Location: Chico, CA. USA
Posts: 5639

Dr. Slack wrote ...

Props have an rpm limit based, along with other things like flutter stability, on their strength. If you add mass to the tip, it would be a very good idea to re-qualify the rpm you can drive it to. It's a shame that the best place to add mass to if you want the best increase in inertia for the least increase in total mass is the worst place mechanically for prop integrity.

yes i know, its a mutually exclusive condtition thats driving me to my psychiatrist!

Dr. Slack wrote ...

Have you considered modifying the time constants in the controller so it *looks* like the motor+prop has more inertia. That will weigh nothing, leave the prop full strength, and allow you to tune the extra inertia quickly. That's if you have access to the appropriate node to add the function.

Oooooo! im inerested please elaborate on this idea, as i have a Ph.D in math and physics guy, and access to all programming through Arduino.

WaveRider

Thu Feb 14 2013, 10:27AM

Registered Member #29 Joined: Fri Feb 03 2006, 09:00AM
Location: Hasselt, Belgium
Posts: 500

Add a function that controls the "spin up" and "spin down" of the prop motor that simulates the effect of extra inertia by adding "slack" to the motor speed control. How you do this depends on the feedback system used in the motor speed control. Maybe this could be as simple as changing parameters in the motor control functions. You can then fool the flight controller into "thinking" that the props have more rotational inertia than they actually do.

Steve Conner

Thu Feb 14 2013, 11:46AM

Registered Member #30 Joined: Fri Feb 03 2006, 10:52AM
Location: Glasgow, Scotland
Posts: 6706

What? Surely from a control point of view, that would only make matters worse by reducing the loop bandwidth. The faster the motors respond, the more stability margin your loop will have.

Let's take a step back... Patrick, why do you want to increase the inertia in the first place? Are you hoping to get more control authority through some sort of gyroscopic effect?

Months ago I expressed the concern that this two-rotor design wouldn't have enough control authority in the pitch axis no matter what you did, and I stand by that. I'm surprised you got it to hover as well as it does in the video.

WaveRider

Thu Feb 14 2013, 12:13PM

Registered Member #29 Joined: Fri Feb 03 2006, 09:00AM
Location: Hasselt, Belgium
Posts: 500

Steve, you are probably right about the gyroscopic effect..i didn't think about that. Indeed it probably is a gyroscopic effect that adds stability to the two-rotor design, since the pitch angle becomes more strongly coupled to the other attitude angles (more specifically, the roll angle..) with increasing gyroscopic effect.

Regarding the motor response, adding slack will require adjusting the control loop gain as well as the position of the dominant loop zero to keep the stability margin within limits. The narrower loop bandwidth will certainly make the system more sluggish to sudden changes on the input..perhaps an undesireable situation.

Patrick

Thu Feb 14 2013, 06:34PM

Registered Member #2431 Joined: Tue Oct 13 2009, 09:47PM
Location: Chico, CA. USA
Posts: 5639

Steve Conner wrote ...

...Let's take a step back... Patrick, why do you want to increase the inertia in the first place? Are you hoping to get more control authority through some sort of gyroscopic effect?

Months ago I expressed the concern that this two-rotor design wouldn't have enough control authority in the pitch axis no matter what you did, and I stand by that. I'm surprised you got it to hover as well as it does in the video.

yes, this is the oblique-active-tilting (OAT) type. the previous version you saw were the FAAT type (fore-aft-active-tilting)... ive had this one 6 feet up totally level and fully controlable, off camera of course! dam it.

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