go_away

### Author Topic: motor physics question  (Read 2968 times)

0 Members and 1 Guest are viewing this topic.

• Supreme Robot
• Posts: 11,680
##### motor physics question
« on: January 14, 2008, 11:54:24 AM »
I have a question that maybe you physicists out there can solve. My boss asked me to quantify this but I'm not sure how.

So I have a motor that rotates 180 degrees, then returns back to 0 degrees. Then reverses itself back to 180 degrees again. This loop repeats indefinitely as fast as possible. The goal is to plot the number of loops possible vs. motor size vs. energy consumption.

Its basically a scaling problem, how does motor size relate to energy use and frequency? Does it scale linearly or cubicly, and how?

The issues I am aware of:
Scaling up increases mass, hence increases rotational momentum. So if you double the size, you double the force, but you also increase the resisting momentum.

There is also electrical inductance. For a motor to rotate you create a big magnetic field. To reverse you must not only destroy that field, but create another with the opposite polarity. Increasing motor size increases this field.

Lets assume a perfect theoretical motor with a big mass on the output shaft.

#### paulstreats

• Supreme Robot
• Posts: 1,381
##### Re: motor physics question
« Reply #1 on: January 14, 2008, 12:23:36 PM »
There is another level to look at in the resisting momentum.

ideally the extra energy that you put into a larger motor would become potential inertial energy for when the motor is switched off, so in theory a 2 pound shaft would need double the energy but for half as long as a 1 pound shaft to both move rotate the same distance- meaning that they both use the same amount of energy.

Are you with me?

The problem arises when you have to reverse the power in order to stop the motor. The 2 pound shaft would need twice the energy to start and twice the energy to effectively stop as the 1 pound shaft.

Basically I would plot a line chart using the loops as frequency and the energy consumption as amplitude to start with.

My next step would be to look at real world examples. Find the stall current for different weights because basically, when you reverse the current to stop the motor, you are effectively stalling it.

Im not sure wether motor size would effectively be quantified with the loop frequency(speed?) - more likely the operating voltage of the motor is what you need to include here?

I'll have another think later....

----edit----

it will be difficult to do a "rule of thumb"system along these lines because different motors have different amounts of windings in their coils depending on model/manufacturer.
« Last Edit: January 14, 2008, 12:30:04 PM by paulstreats »

#### SmAsH

• Supreme Robot
• Posts: 3,959
• SoR's Locale Electronics Nut.
##### Re: motor physics question
« Reply #2 on: January 14, 2008, 07:23:23 PM »
hmm...well i havent done this in psysics yet....but i'd say there are more than one answers for this but you seem a lot older than me but i hope this helps.....the motor size generally needs you to provide a higher voltage...and uses more energy..but again there are many answers depending on torque voltage input power...hope this has helped you a bit....anyways toodle oo

~smash
Howdy

#### airman00

• Contest Winner
• Supreme Robot
• Posts: 3,653
• narobo.com
##### Re: motor physics question
« Reply #3 on: January 15, 2008, 06:27:43 AM »
hmm...well i havent done this in psysics yet....but i'd say there are more than one answers for this but you seem a lot older than me but i hope this helps.....the motor size generally needs you to provide a higher voltage...and uses more energy..but again there are many answers depending on torque voltage input power...hope this has helped you a bit....anyways toodle oo

~smash

ehhh, motor size is incredibly vague and it is not always true that the size has a linear relationship with voltage
Check out the Roboduino, Arduino-compatible board!

www.Narobo.com

#### paulstreats

• Supreme Robot
• Posts: 1,381
##### Re: motor physics question
« Reply #4 on: January 15, 2008, 06:36:39 AM »
because you are having to brake / stop the motor, then the energy wasted / lost in the braking process is equal to the energy required to start the motor.

so.....

psuedo speaking

a motor of 1 pound shaft with 200 windings uses 10v at 4 amps = 40w. to move at 10rpm and only pulling its own weight. In order to stop you would lose 40w.

a motor of 2 pound shaft with 400 windings (and twice the size) uses 20v at 3 amps = 60w. to move at 10rpm and only pull its own weight. (I think the inverse square law affecting the magnetic fields means that the greater the field produced by the larger motor, the less less energy it would need - or that the magnetic field increases in squares) - it just takes longer to build up the field.

The thing is that the larger motor does take more energy and so when you stop it, you are wasting more energy, it should also take longer to stop (in squares) and also longer to start(in squares)as the magnetic field build up.

conclusion.

Larger motors are more efficient torque wise but it takes longer to build up the magnetic fields.

smaller motors start faster and stop faster.

Obviously the rotational momentum is proportional to the weight of the shaft and the load, so the smaller motor also needs less energy to stop than the larger motor, and also can stop faster.

« Last Edit: January 15, 2008, 06:37:50 AM by paulstreats »

#### airman00

• Contest Winner
• Supreme Robot
• Posts: 3,653
• narobo.com
##### Re: motor physics question
« Reply #5 on: January 15, 2008, 06:42:11 AM »
that makes sense
Check out the Roboduino, Arduino-compatible board!

www.Narobo.com

• Robot Overlord
• Posts: 293
##### Re: motor physics question
« Reply #6 on: January 15, 2008, 08:02:03 AM »
I am interested in your problem. But first of all I want to say that I have never dealt with such a situation so I consider myself a noob in this area.

Now let me see if I understand what you want: you want a 2D graph that shows the relation ship between the number of loops(n) and the size of the motor(m, and I assume that it is the not the size of the motor but the force necessary to move the object connect to the output shaft), and the energy consuption(E). The energy is a function of the motor so E(m). But instead of using m I would use the angular momentum.I=m*r^2

In that case, in order to fully solve the problem I need another variable: the angular speed of the motor(w).
That is because E=mv^2/2=Iw^2/2.

And there is another problem: you asked to consider the motor an ideal motor. in that case friction=0, perfect mechanical structure(dont fall apart), no mass, no size and number of possible loops=+infinity.

I pesonally cant solve the this problem under those conditions. But I can give you the hints you want:

Its basically a scaling problem, how does motor size relate to energy use and frequency? Does it scale linearly or cubicly, and how?

energy and motor size relationship:
E=I*w^2/2,   I=Imotor + Iweitgh. So it scales linearly.
(     /
I=|m*r^2dr
/            )

energy and frequency:
E=I*w^2/2;   w=2*pi*f ->  E=2*pi^2*I*f^2. So it scales squarely(dont know if this word exists )

Scaling up increases mass, hence increases rotational momentum. So if you double the size, you double the force, but you also increase the resisting momentum.

There is also electrical inductance. For a motor to rotate you create a big magnetic field. To reverse you must not only destroy that field, but create another with the opposite polarity. Increasing motor size increases this field.

Because of that the amount of energy required is 2 times the amount I wrote before. Hence E=4*pi^2*I*f^2.
E=2*pi^2*I*f^2 for stopping E=2*pi^2*I*f^2 for accelerating in the opposite direction.

That is everything I can say under the given conditions. Sorry but mechanics is not my field so there might be some variables relataded to motors that I am not counting. Good luck with your boss.
A.I.(yes those are my initials)

#### airman00

• Contest Winner
• Supreme Robot
• Posts: 3,653
• narobo.com
##### Re: motor physics question
« Reply #7 on: January 15, 2008, 08:19:53 AM »
all these have to be taken into account:  number of windings(and the gauge of that wire) , the weight of shaft, friction

The actual mass of the motor may not have an effect on it, since the majority of the weight can either be the casing, the winding, or the shaft.
Check out the Roboduino, Arduino-compatible board!

www.Narobo.com

• Supreme Robot
• Posts: 11,680
##### Re: motor physics question
« Reply #8 on: January 15, 2008, 08:28:48 AM »
paulstreats you make a good point . . . if I don't scale the voltage with the motor size, then the motor will obviously be slower as it gets larger . . .

there are soooo many variables to consider . . . Ill sit down and read some wikipedia for awhile and see if I can derive some scaling equations . . .

or just buy a bunch of motors and run experiments . . .

• Robot Overlord
• Posts: 293
##### Re: motor physics question
« Reply #9 on: January 15, 2008, 06:27:05 PM »
all these have to be taken into account:  number of windings(and the gauge of that wire) , the weight of shaft, friction

The actual mass of the motor may not have an effect on it, since the majority of the weight can either be the casing, the winding, or the shaft.

The number of windings is just important to determine the torque of the motor. By the torque you calculate the angular accel. and thus the angular speed. It is implicit in the calculations.
The mass of the shaft(not weight) is used and it is the moment of inertia of the motor in my calculations.
Friction, air resitance and electric resistance are important but there is no data about them.
I was thinking about the problem yesterday and I found something I didnt get: How is the motor suposed to break. Is the shaft going to break in two or are the wires in the windings going to burn? For the shaft you will have to calculate the twist caused by the stress(and tables for properties). For the wires you need not only the power consumed but also the temperature and a bunch of tables with the properties of various wires. I give up! I will need a super computer to run such a simulation.
A.I.(yes those are my initials)

#### paulstreats

• Supreme Robot
• Posts: 1,381