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# Reaction Wheel with a DC motor

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#### m.mahdi_sh

##### New Member
hello there
i'm new to the forum and i'm here for a project i'm doing.
u've probably seen some reverse pendulum or small bicycle with Reaction Wheel which can stay balanced. here is a pic of what i mean:

rn, i'm trying to choose a DC motor for driving the reaction wheel, i've used matlab simulink to simulate a LQR controller with the system and since i don't have a motor yet, i can't add a dc motor model to the simulation(because the datasheet usually don't give required parameters!)Long story short i have a simulation of the dynamic system without the dynamics of the motor and it has given me a Torque and speed for Reaction Wheel
i've got series of Qs:
1. as we know, the motor generates torque as needed! meaning that u should WANT the torque for the motor to give it to u! so how does all this come together?
first, my reaction wheel "mass" and "I" are constant(the reaction wheel physical properties don't change)
second, we know that "T=I*alpha", which is the basis of the simulation equations that finally will be reported as the Torque mentioned above
so how does this "wanting the torque to get one" and this "constant "m" & "I" of reaction wheel" and this "T=I*alpha" come together?!?!?

2. generally speaking, it is the "alpha"(change of speed) that gives the torque(T=I*Alpha); and in no datasheet have i ever seen that kind of data; all i get is nominal T and rpm and some no load(and Full load) speed & current
with my understanding the "alpha" is as follows:
alpha=Dw/Dt(delta omega(rotational speed)/ delta time)
i know that "Dt" has got smth to do with the time constant of the motor and stuff, but i'm clouded about that!(which unfortunately the datasheets don't provide, i know i can measure it once i have the actual motor, but i to first choose a motor based on what i have!!)
my question is, is there any way to calculate this alpha for a motor with the basics of the datasheets(being nominal Torque & Speed)? or just a way to get a feeling of which motor will have a better alpha(meaning it would be faster to reach the required speed)? should i go for a more torque(hence low speed) motor or a high speed(hence low torque(just enough to turn the wheel which isn't going to be that much i suppose!) motor?

i'm really sorry for the long gibberish kind of Question! i'm really confused about the whole thing!

A suitable DC motor would be one designed for the servo market, I built the Picmicro demo reverse pendulum version from the APP AN-964note.
Ideally the servo variety have some extra characteristics, higher pole count, skewed rotor laminations etc.

I'd look at the "Stall torque" figure for any motor you consider.

Also look a geared motors, with fairly low gear ratio gearboxes, eg. 10:1 up to possibly 20:1 or 25:1 would be fine at a guess.
In that case the motor torque is multiplied by the gear ratio.

There are some good reasons for using gearing:
You likely do not want the reaction wheel being capable of spinning up to several thousand RPM, which a small "bare" motor likely does.

The motor torque is multiplied, so more torque at the output.

And, the inertia of the load as seen by the motor is reduced by the square of the gear ratio.

That means you should get a much faster load response for a given size (& power) motor.

Full load of a motor is controlled by motor heating. You will probably be running the motor at low speeds, and intermittently, so the stall torque is what you are interested.

Most DC motors will have the torque proportional to the current. The speed will reduce linearly as the torque goes up, if the voltage supply is constant.

I'd look at the "Stall torque" figure for any motor you consider.

Also look a geared motors, with fairly low gear ratio gearboxes, eg. 10:1 up to possibly 20:1 or 25:1 would be fine at a guess.
In that case the motor torque is multiplied by the gear ratio.

There are some good reasons for using gearing:
You likely do not want the reaction wheel being capable of spinning up to several thousand RPM, which a small "bare" motor likely does.

The motor torque is multiplied, so more torque at the output.

And, the inertia of the load as seen by the motor is reduced by the square of the gear ratio.

That means you should get a much faster load response for a given size (& power) motor.
thank you for the response!
i didn't get the last part! how does that means i get a faster load response?! u mean if i use a higher torque rating motor, the response would be faster? is that what u r implying?

Full load of a motor is controlled by motor heating. You will probably be running the motor at low speeds, and intermittently, so the stall torque is what you are interested.

Most DC motors will have the torque proportional to the current. The speed will reduce linearly as the torque goes up, if the voltage supply is constant.

yes that is right. it stops several times and reverse the rotation. i know that the stall torque must be low to get a better performance, yet i can't usually find that neither!
they give nominal voltage, Torque, current
no load speed and current
maximum Torque

is there a way to determine the stall torque of the motor with these info?

i know about torque and speed combination and the current. what i'm concerned is not the "speed" but rather the "acceleration" of the motor. that is the thing which would produce the torque

thank you for the response! really appreciate it

can u answer my 1 & 2 Qs specifically?

they give nominal voltage, Torque, current
no load speed and current
maximum Torque
maximum torque may be another name for stall torque.

What are the values that they quote?

There are generally two rating curves throughout the RPM range for motor used in these kind of applications.
One is the Continuous torque level and for most motors is maximum at zero rpm.
The other is the maximum Momentary torque where it is possible to enter this level only for a very short period of time without damage to the motor.

My experience with DC gear motors must be different than the rest of you guys. The gearing to me always seemed to make reversal take longer, due to the clearances needed in the gear teeth and the inertial of the gear train.

The motor in the photo looks more like what Max said a DC servo motor because most I've seen have that box for the wire connections.

The TS doesn't say how big this is going to be. For something small wouldn't a stepper motor be a viable idea? Instant reversal with no brushes and commutator segments to worry about like in a normal DC motor, they don't like to be reversed instantly for any amount of times doing it.

i know that the stall torque must be low to get a better performance,
You need HIGHER stall torque for better performance!

When you drive a load through a gearbox, the maximum torque at the load is whatever the motor can provide multiplied by the gear ratio.
For your application you need a fairly low ratio so the motor does not take ages to get to high speed just to get the load moving, ie. a fast response at the load.

However, you also need to be able to accelerate the flywheel very quickly to get a good overall control response.

That's where the gearbox helps again. How fast the flywheel can be accelerated depends on the inertial load "seen" by the motor.
That is reduced by the _square_ of the gearbox ratio.

eg. If the motor direct could only accelerate it a 10 RPM per second, just a 2:1 gearbox would allow the motor to accelerate it at 40 RPM per second. 3:1 should allow 90 RPM per second etc.

My experience with DC gear motors must be different than the rest of you guys. The gearing to me always seemed to make reversal take longer, due to the clearances needed in the gear teeth and the inertial of the gear train.
In accurate applications such as CNC/motion/positioning control etc, the planetary GB is usually used as it is generally the one with the lowest backlash etc.

In accurate applications such as CNC/motion/positioning control etc, the planetary GB is usually used as it is generally the one with the lowest backlash etc.
Timing belt drives are also very common for CNC axis movement, as they can be effectively zero backlash but at a far lower cost than the precision gearboxes.

maximum torque may be another name for stall torque.

What are the values that they quote?
exactly, i was thinking the same, i'm thinking about a motor with smth like 1.5 or 2 Kg.cm torque
which i am looking at some dc motors coupled with a gearbox which is a 600 rpm at output /1.5 kg.cm(nominal) /12 V/2 kg.cm(max(or probably stall torque)

There are generally two rating curves throughout the RPM range for motor used in these kind of applications.
One is the Continuous torque level and for most motors is maximum at zero rpm.
The other is the maximum Momentary torque where it is possible to enter this level only for a very short period of time without damage to the motor.
if i had any curve for these i would be pleased! these Chinese motors just give out those nominal things i said!

My experience with DC gear motors must be different than the rest of you guys. The gearing to me always seemed to make reversal take longer, due to the clearances needed in the gear teeth and the inertial of the gear train.

The motor in the photo looks more like what Max said a DC servo motor because most I've seen have that box for the wire connections.

The TS doesn't say how big this is going to be. For something small wouldn't a stepper motor be a viable idea? Instant reversal with no brushes and commutator segments to worry about like in a normal DC motor, they don't like to be reversed instantly for any amount of times doing it.
that thing at the back of the motor is where the encoder is located! and i have seen the complete video, they use a dc motor with an encoder!
my model is going to be small, smth like 160 mm tall, 60 mm wide and 300 mm long
i don't thing stepper motor would be adequate cause they are like just for the precision and stuff as mentioned in the other's posts!
there is a possibility to use a brushless motor but finding a low KV brushless is kinda hard so the next best option is dc motor

You need HIGHER stall torque for better performance!

When you drive a load through a gearbox, the maximum torque at the load is whatever the motor can provide multiplied by the gear ratio.
For your application you need a fairly low ratio so the motor does not take ages to get to high speed just to get the load moving, ie. a fast response at the load.

However, you also need to be able to accelerate the flywheel very quickly to get a good overall control response.

That's where the gearbox helps again. How fast the flywheel can be accelerated depends on the inertial load "seen" by the motor.
That is reduced by the _square_ of the gearbox ratio.

eg. If the motor direct could only accelerate it a 10 RPM per second, just a 2:1 gearbox would allow the motor to accelerate it at 40 RPM per second. 3:1 should allow 90 RPM per second etc.
now i'm getting it i think! so when the motor start rotating(or reverses) i would get the stall torque yeah? and after start of the rotation that acceleration would come in play?

the last paragraph actually solves my problem then! so for a certain flywheel with constant "I" with a high ratio i'll get a high "alpha" so i'll get a better torque
thanks

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I'd try with something like one of these (1000 RPM version) to start with; they are geared but still with a high output speed, so hopefully a suitably low ratio for fast acceleration.

Timing belt drives are also very common for CNC axis movement, as they can be effectively zero backlash but at a far lower cost than the precision gearboxes.
The only place I have seen that used, and used myself is on axis where very fine resolutions are not really required, all the Industrial mills & lathes I have worked on used direct drive or some zero backlash method, e..g. the planetary GB is virtually zero back-lash or if any at all it is a constant, unlike timing belt..
The hobby CNC versions maybe use this for low cost.

The hobby CNC versions maybe use this for low cost.
The other end of the scale - very large machines, including high precision ones.
They are standard on such as Elamills, CME floor borers, W&B Millennium, Morando VBs and many others.

Example, on a Morando VB being stripped for relocation - the X drive and also under the thin vertical motor, one linking that to the tool carousel.

This is an interesting problem. We've been looking (at school) for a suitable system to teach PID feedback and a stationary balance project like this fits the requirements well. How will the tilt of the bike be measured? If an accelerometer is used then, on a normal turn, gravity will still be through the center line of the bike just a little stronger and direction of tilt not determinable. A small gyroscope may be the solution. I'll be following this thread with interest.

Mike.
Edit, put PWM when I meant PID. Doh.

Last edited:
This is an interesting problem. We've been looking (at school) for a suitable system to teach PWM feedback and a stationary balance project like this fits the requirements well. How will the tilt of the bike be measured? If an accelerometer is used then, on a normal turn, gravity will still be through the center line of the bike just a little stronger and direction of tilt not determinable. A small gyroscope may be the solution. I'll be following this thread with interest.

Mike.

Your school sounds much more of a fun place than mine was!

Your school sounds much more of a fun place than mine was!
It's not actually the school doing this but an after school robotics/programming club. But, yes, definitely more fun than my school.

Mike.

This is an interesting problem. We've been looking (at school) for a suitable system to teach PID feedback and a stationary balance project like this fits the requirements well. How will the tilt of the bike be measured? If an accelerometer is used then, on a normal turn, gravity will still be through the center line of the bike just a little stronger and direction of tilt not determinable. A small gyroscope may be the solution. I'll be following this thread with interest.

Mike.
Edit, put PWM when I meant PID. Doh.
well we are in the early stages somehow, still not on the construction part yet but it'll probably be a normal tilt sensor used in smart phones these days
but according to my dynamic equations i'll probably need the rotational speed of the motorcycle and the reaction wheel
for the reaction wheel i'll use an optical encoder directly watching the wheel(which would have strips for the resolution of the encoder)
but for the motorcycle i think i will need an accelerometer or smth rather than normal tilt sensor

it will not include a coupled complicated control system adding movements of the steering and the motorcycle, from what i am working on, the stationary control system would be adequate for a moving motorcycle as well.

PS: my control loop is actually just using the angle of the motor cycle and then takes a derivative of the theta(angle of the motorcycle) and it's a university b.sc project

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