Gearbox -physics related question

[sporno]

So Ive been doing alot of thinking, and a bit of research about decreasing rotational mass and decreasing rotational inertia.

For example ( example guys , this is all theory)

if F=MA

and lets say F is 10HP ( horsepower , which is derived from torque)
and M= 2 lbs ( lets say a gear , i know heavy , but my motorcycle if any of you guys remember my thread on the bike had a 7 lb rear sprocket)

And lets say that A is 2,000 RPM ( yes i know its not actually RPM )

ok so if the mass decreases , but the force stays the same wouldn't the RPM go up ... in theory

ok now on to the decreasing rotational inertia.

So on a gear , or any kind of rotating object , there is more torque on the outer part of the gear , as in a friction drive , the closer to the center the more HP , the closer to the outside the more torque.

but if the mass closer to the outside was decreased , rather than the inside closer to the center , wouldn't it take less initial power to move the object?

This is all just stuff Ive been thinking about.

Now how this relates to Gearboxes

If i cheesed a couple of the gears in the AM , or KOP gearboxes , decreasing rotational inertia , and rotational mass , would that have any effect aside from just cutting weight?


would it actually put more power to the ground , and create less drive train power loss?

Also in cars , people make much more power to the wheels , but getting a lighter flywheel.

So please tell me your thoughts and dont flame this too much

[techtiger1]

Sporno what your saying is all right for the most part. However relating to the AndyMark/FIRST application gearboxes the mass is so light that even lighting a gear by say a lb which is tough to do in a well designed gearbox, won't make a huge diffrence. Also when considering F=M*A and initial power you have to look at what your motors can do in comparison to the force they can put out and the object they are moving. Run some numbers on that theory with the CIMS and tell me if your still worried about them spinning anything less then 2lbs. Lighting the gear does make a diffrence by putting less load on the motor but in this application it is only a slight diffrence and generally a bigger worry is weight more so then power. My advice would be to test it if you really think it's worht the time and effort.

-Drew

[thefro526]

In my understanding (in no way am I an expert) When you decrease the mass of an object and the force stays the same said object takes less time to spin up to speed and i think because less force is need to spin said object it is transfered to the drive or what ever.

when I built a vex shooter a while back I had 3 motors using a 1:49 gear ratio which had theoretical rpm of 4900. I hit no where near that. But originally i used normal 2.75 inch wheels with rubber on them. They took super long to spin up to speed, but when i replaced thouse wheels with omnis they took much less to spin up to speed and also may have spun a bit faster.

hope this helps,
Dustin

[sporno]

yes , i totally understand that the decreasing the weight is more important , im just trying to figure out, is is there a better way to cut the weight.

Also if rotational mass of the gear , sprocket , some round object , is decreased its less stress on the motor to get it initially moving , so it takes less rotational inertia to move it , so wouldn't that increase " throttle response " too?

And this isn't just for the gearboxes , its anything really , lets say a shooter for the AIM HIGH game. If the motor puts out so much power and , then you loose so much power in the drive train mechanism , if the motor didn't have to work as hard to move the wheel or drive train , it would spin faster , and shoot farther ....... right?

this is more of my theory

im in physics 1

[techtiger1]

Yes your right in theory, the lighter the rotating object is the less energy is used to spin it (in this case) making the whole system more efficient. What I am asking you to do now is to put the principle in practice I think you'll find that in a application for FIRST where components are generally light (not a steel vs. alumnium flywheel) you will see only a slight diffrence in proformance but a difference none the less. Good ideas really everything you've said has a viable point.

[Madison]

I'm going to caution you to, as you start to think more about how these different concepts are related, be sure that you're using appropriate units to describe each of the elements present in your equations. If an equation involves a force, use newtons (or lbf.), etc. You've got an awful jumble of crossed wires to start with here, describing force in terms of power or torque and acceleration with velocity.

You'll help us to understand your questions better and you'll understand our explanations more because we'll all be speaking the same language, so to speak.

[techtiger1]

Thank you Madison ! yes proper notation is always important you beat me to that one.

[sporno]

i was throwing it out there in theory, next time ill try and clear it up , i think it seems simpler using the terms i threw out there rather than lots of numbers and different units .. for theoretical stuff atleast , its all an idea

[Alex.Norton]

If you had two identicle systems (wieght, support...) and two wheels that have the same weight but wheel A has less rotational inertia than wheel B, then no, they would spin up to the same speed. However wheel A will take less time to get up to speed than wheel B. However, if you got both wheels up to speed turned off the power, then tried to shoot a ball with the momentum of the wheel (say in 2006), wheel A would shoot fewer balls than wheel B.

In reallity wheel A or gear A would probably also wiegh less, so would put less strain of the system and it might be better balanced which would also reduce stress and so on. So in a real system like a shooter the rotational inertian of the wheel would have a huge effect on the efficiency of the system.

However in a drive train the gears shouldn't be big enough to make a difference. So I will calculate the time it would take the first big gear in the am planetary to spin up. This gear spins at 1540 RPM or 161.26 Radian/sec

m = ~.31kg
w (omega) = 161.26 Radians/sec
I = (mr^2)/2 = 1.562 E-4
T (average) = ~3.95 Nm

in this cas Torque (T) = Moment of Inertia (I) * angular acceleration (a)
so a (alpha) = T/I = 25280 Radians/sec^2

angular velocity (w) = angular acceleration (a) * time (t)
so t = w/a = .00636 seconds

A 120 pound robot (I know its actaully more like 133 lbs) with a reduction of 1:12.75 (AM single speed) to a four inch wheel on the other hand will take:

m = 54.54 kg
F (average) = ~138.04 N
a = F/m = 2.531m/sec^2
vFinal = 2.295 m/s
t = v/a = .907 seconds

So the gear wil take .00636 seconds to spin up and the robot will take .907seconds to accelerate (under absolutely idea situations). There are some assumptions in this. If anyone thinks these assumptions are too extreme, sees a mistake in my math or wants to know where I got a number please PM me.

So since the time of acceleration of the bot is huge compared to the gear it really doesn't make a difference. However you can see that the gear would slow the robot down a little.

In the case of a car there is a much bigger difference because your talking about a 50 lbs fly wheel not a half pound gear. So your theory is correct but I would always sugjest doing to math cause you'll see if you actaully need to think about implimenting it. To do this you should calculate the acceleration of the robot with two different gears (one lightened, one not) and see if there is a difference.

hope that helps
Alex

[Qbranch]

Bzuhhh... Just making sure... In your conceptual post you're ok...

But as stated above (and its so important i'll restate it) F is a force. Hp is a rate of energy conversion. 2000RPM is a speed, while 2000RPM/s is an acceleration. 2 lbs is a force, while 0.0622slugs or 0.9072kg is a mass.

And, to reaffirm, yeah the rotational inertia of the AM gearbox is negligable... as well as the rest of your drivetrain (unless you have some gigantic flywheel your storing energy in). Just worry about the mass of your robot.

-q

[Alex.Norton]

Also, I hadn't thought enough about your theory above, and no it is not actually true. Lightening the gear would not speed up the output.

The limiting factor in the speed of the system is the max RPM of the motor which is a result of motor design. The CIM won't spin any faster than ~5200 RPM or so even if there is no pinion gear or drive train or anything.

When I calculated the time above I was using your equation F = m*a. This relates to a force, a mass, and an acceleration. acceleration is only applicable to speed when introduce time. The reason that the motor won't spin the gear faster is because as the output RPM of the motor increases the torque decreases to 0 at the max RPM of the motor.

Again, hope it helps
Alex

[techtiger1]

Alex is correct. Thats why I said in theory that this idea works but there is a limit too it.

[Kevin Sevcik]

As noted, the rotational inertia of most all gearboxes in FIRST are negligible. And if you lightened the gearbox with everything else the same, your max speed would remain the same, though the robot would accelerate slightly faster. The best way to think about it is as a division of kinetic energy. Assuming you have a flywheel attached such that it spins faster the faster your robot moves, the flywheel would store some amount of rotational kinetic energy for every Joule of translational kinetic energy stored by your robot moving forward. With a standard gearbox, it's probably something like .01 J of rotational energy for every 1 J of translational. With a big flywheel, you'd be storing more in the flywheel, and a comparatively smaller amount of every J from your motor would be going towards actually moving the robot forward.

To correct one error I've sen in this thread. The top speed of your robot does not depend on the max RPM of the motor. It depends on the friction in your drivetrain. The friction represents a torque that must be subtracted from the torque developed by the motor before you start firguring the acceleration of the robot. So at some point, the torque put out by the motor equals the friction torque, and your robot stops accelerating. Since the motor is putting out mre than zero torque, this isn't going to be the no-load speed.

[sporno]

ok thanks for all the help

once again this is all just theory, im just trying to find out if what im saying is even ballpark

and this isnt just in relation to the gearboxes , but any rotating object on the bot.

Also , if the drive train is more efficent , less power is lost , and more gets to the wheels , thus some power is picked up .... right

[Alex.Norton]

Originally Posted by Kevin Sevcik

As noted, the rotational inertia of most all gearboxes in FIRST are negligible. And if you lightened the gearbox with everything Since the motor is putting out more than zero torque, this isn't going to be the no-load speed.

This all depends on how you define your motor. Technically no motor has a no load speed since the motor has to spin itself which takes some power input. Since the CIM has a resistance and you have to put power in which means that your producing power somehow. I think you could define the whole drive train as a motor, maybe a linear motor, and then say that the top speed of the robot is the free speed.

A lot of solving a problem in physics is just choosing the correct frame of reference and it might be easier to define the drive train as the motor and just measure its speed. I'm not sure what the use of this is but hey...

Alex