Reflected Inertia?

[archiver]

Posted by ChrisH at 04/24/2001 11:27 AM EST


Engineer on team #330, Beach 'Bots, from Hope Chapel Academy and NASA JPL, J & F Machine, Raytheon, et al.



Can any of you motor gurus tell me what this is and how to calculate it? None of our technical people have ever heard of it.

Chris Husmann, PE
Team 330 the Beach'Bots

[archiver]

Posted by P.J. Baker at 04/24/2001 12:29 PM EST


Engineer on team #177, Bobcat Robotics, from South Windsor High School and International Fuel Cells.


In Reply to: Reflected Inertia?
Posted by ChrisH on 04/24/2001 11:27 AM EST:



I'm not truly a motors guy, but it goes something like this:

The reflected inertia is the inertial load that the motor sees through the system's drive train.

Taking a robot as an example, and looking at it from the wheel (the end of the drive train) a torque must be exerted on the inertial load of the robot to achieve angular acceleration of the wheels (Torque = J (inertia) * alpha (angular acceleration)) which will result (with good traction) in linear acceleration of the robot.

Because of the mechanical advantage of the drive train (equal to the gear reduction), the inertia that the motor actually "sees" is much smaller than the inertia that you would feel if you personally tried to move the robot by turning its wheels. To the best of my knowledge, this reduced inertia is known as the "reflected inertia" of the system.

Please note that I've simplified things a bit here, and probably left a thing or two out, but I believe the basic concept is right. In designing sytems with motors, people will often try to match the motor inertia (armatures, windings, etc.) to the reflected inertia of the system. I think that this is basically analogous to impedance matching in electronics design.

Hope that helps. I also hope that someone like Joe J. who works w/motors on a daily basis comes along and does the expanation a little more justice than I did.

P.J.

[archiver]

Posted by Paul Copioli at 04/25/2001 1:00 PM EST


Engineer on team #217, Team Macomb - Royal Fusion, from Utica Schools, Fraser Schools, Warren Cons. School and Ford Motor Company.


In Reply to: Reflected Inertia?
Posted by ChrisH on 04/24/2001 11:27 AM EST:



: Can any of you motor gurus tell me what this is and how to calculate it? None of our technical people have ever heard of it.

Chris,


I am an engineer at FANUC Robotics (Roch Hills, MI) and I work with servo motors every day. Reflected inertia is especially important when dealing with servo motors in order to manage control system stability. Anyway, P.J. is correct about reflected inertia, but I will get more specific.

Let's take a motor connected to a spur gear set with a 4:1 ratio (pinion pitch diameter is 25mm and output gear is 100mm). An arm is attached directly to the output gear and has a length L with a mass Marm. The arm has an inertia about its CG, Iarm and the CG is located at L/2. The inertia at the spur gear output is Itot=Iarm + Marm*(L/2)^2. That, however, is not the inertia seen at the motor.

Itot@mot = Itot/(GR^2) 'Inertia seen at motor

GR is the gear ratio. I define gear ratio as the number of turns of the MOTOR per 1 turn of the output.

The output gear also has an Inertia which needs to be reflected in the same way (Igear@mot = Igear/[GR^2]).

If you have multiple stages, then each stage is reflected to the previous stage by dividing the inertia by (GRstage^2).

After the Inertia from each component is reflected to the motor, you add them all up and compare the total reflected inertia to the motor rotor inertia. Like P.J. said, ideally, you would like to keep the ratio at 1:1, but most digital servo motors can handle 10:1 Load to rotor ratio.

If you are using pots for arm feedback on FIRST robots, we have found that minimizing the load-to-rotor ratio helps in controllability.

Any questions or if you want the derivation, just ask.

-Paul

[archiver]

Posted by ChrisH at 04/25/2001 1:59 PM EST


Engineer on team #330, Beach 'Bots, from Hope Chapel Academy and NASA JPL, J & F Machine, Raytheon, et al.


In Reply to: Re: Reflected Inertia?
Posted by Paul Copioli on 04/25/2001 1:00 PM EST:



Paul,

No need for the derivation. I'm having enough trouble remembering how to calculate inertia after all these years. So I'm not sure I would understand it anyway.

Reflected inertia seemes to be one of those terms that needs no explanation because "everybody" already knows what it is.

But you answered the question with a remarkably appropriate example. I'm going to print it out and start working on a design spreadsheet right away.

One of our goals for the off season this year is to build an arm that we can tell to go to a specific position, and then have it stay put.

Unfortunately, none of us works with servo-design. My knowledge is restricted to using model airplane type servos.

Thanks for the help

Chris Husmann, PE
Team 330 the Beach'Bots

[archiver]

Posted by Tom S. at 04/26/2001 8:53 PM EST


Student on team #177, The Bobcats, from South Windsor High School and International Fuel Cells.


In Reply to: That's what I was looking for
Posted by ChrisH on 04/25/2001 1:59 PM EST:



Chris,

Couldn't you just do this by adding a potentiometer to the arm's pivot point, and using software to get it to go to a set position? we did this successfully in florida, i wrote code that on every loop it checked to see what position the arm was at through the potentiometer, and if it was too high or too low it set the motor speeds accordingly...

This may or may not be what you want to do, i'm not really sure what you mean by a servo-design, I put the code that we use to do this on our bot at the bottom of this post... the code looks kind of wierd beucase my code lost its formatting when i posted it. good luck

Tom Schindler
Team 177


if p3_sw_trig = 1 and p3_sw_trig = 1 then armpos
goto noarmpos

armpos:
'This will move the arm until sensor1
'reads 134.

if sensor1 > 134 then armdown
goto skiparmdown

armdown:
if sensor1 128 then armupslow
p4_y = 67
goto skiparmup
armupslow:
p4_y = 114
skiparmup:

noarmpos:

[archiver]

Posted by ChrisH at 04/27/2001 12:23 PM EST


Engineer on team #330, Beach 'Bots, from Hope Chapel Academy and NASA JPL, J & F Machine, Raytheon, et al.


In Reply to: Re: That's what I was looking for
Posted by Tom S. on 04/26/2001 8:53 PM EST:



Tom,

The original post came about as a result of reading several articles in trade mags about positional controls. They all used the term "refected inertia" but none either explained what it was or how to caclulate it. They did state that it was desireable to have it be no more than 10 times the inertia of the motor (which is on at least some of the spec sheets we got at the kickoff).

I knew what inertia was, but reflected inertia was new to me. It was also new to everyone else on our team. So I thought I'd ask for an explanation. The problem is not necessarily the control program, it is more designing a system including the mechanical elements that will perform as intended.

I honestly don't know much about our control program, as I'm a mechanical kind of guy. But a control program that tells the arm to go up when needed, is great, unless you don't have adequate torque or power to move the arm. I'm more concerned with the torque part of things right now. (We can always fix the software later ). But if I can design an arm that makes the control guys life easier, then that is even better.

Chris Husman, PE
Team 330 the Beach'Bots

PS. It's good to see that us Inguneers aren't the only one who read this forum.

[archiver]

Posted by Joe Johnson at 04/25/2001 7:04 PM EST


Engineer on team #47, Chief Delphi, from Pontiac Central High School and Delphi Automotive Systems.


In Reply to: Re: Reflected Inertia?
Posted by Paul Copioli on 04/25/2001 1:00 PM EST:



Paul,

Thanks for the introduction.

I have some questions though.

I have always used either speed consideration or torque
consideration to design my gear ratios, not reflected
inertia.

I why do we want a 1 to 1 ratio?

What good things does it do for us if we can get a 1 to
1 ratio?

Finally, does it make sense to add mass to the armature
of the motor in order to improve the reflected inertia
ratio? If I can get good things for the extra work, I
may end up doing it.

I have always blamed my main problems with controlling
large robot arms on 3 main problems:

1) Inability to easily implement a PID control
algorithm on the current STAMP2 CPU.

2) The dead band in the Victors (a PWM output value of
127 +/- 10% yeilds 0 Volts output -- very annoying).

3) My poor design skills preventing me from properly
counter-balancing the arm so that the arm is more or
less neutrally balanced over a large range of motion.

I try, but weight limits, time limits and incompetent
engineering on my part always have conspired to leave
the arm falling or auto rising over most of its range
of motion.

So...

My question is now, maybe there is some other culprit
that I should be blaming as well.

I am anxious to hear your reply.

Joe J.

[archiver]

Posted by Paul Copioli at 04/26/2001 8:37 AM EST


Engineer on team #217, Team Macomb - Royal Fusion, from Utica Schools, Fraser Schools, Warren Cons. School and Ford Motor Company.


In Reply to: questions from a speed/torque guy...
Posted by Joe Johnson on 04/25/2001 7:04 PM EST:



Joe,

BEWARE! This is a long response due to the nature of your questions and the fact that I can't draw any pictures!!!

I will try to answer your 3 questions, but first I would like to address the 3 problems you mentioned.

: 1) Inability to easily implement a PID control
: algorithm on the current STAMP2 CPU.

--- Yes. This is a big problem, but pretty solvable. Actually, this problem amplifies the need to have a favorable load-to-rotor(LR) ratio, because the control algorithm is limited. Up until about 3 years ago, any machine using a FANUC motor (all of our robots) was required to keep the LR ratio below 3:1 or we would have control problems. As the control system (and encoder resolution) improved, our LR ratios can be as high as 10:1. One last thing about the algorithm: when we use pots for feedback, we add a "velocity gain loop" in our system. The velocity loop is pretty simple: it takes how large your position difference is and reduces power as you close in on the command position. It works great.

: 2) The dead band in the Victors (a PWM output value of 127 +/- 10% yeilds 0 Volts output -- very annoying).

--- Again, Yes. Very annoying. We have learned to deal with it (although, ever since we went to this velocity control loop, the problem is less severe).

: 3) My poor design skills preventing me from properly
: counter-balancing the arm so that the arm is more or
: less neutrally balanced over a large range of motion.

--- Yeah right, poor design skills. What, are you a comedian? Anyway, I have read all the white papers, etc. that you have put out there regarding balancing. I am curious, do you always use the gas shocks? If you do, then it is very difficult to get a perfect balance. There are little gems in the kit called springs --- work great. With a spring you can configure the geometry such that you get a perfect balance for an individual arm. With that said, If you have an inner arm and an outer arm like you guys did this year and we did last year, then you can not perfectly balance the inner arm, because of the position variance on the outer arm. What we do (at FANUC and on Royal Fusion) is take the entire mass of the outer arm (plus payload) and assume it is at the end of the inner arm. If you plot Torque vs. Inner arm angle you can see that the gravity load is sinusoidal. A spring with a constant stiffness can be configured to perfectly match gravity. One last comment on balancing: The arm will not be perfectly balanced because of the outer arm location, but if you point the outer arm straight down; then you will see your arm perfectly balanced. This year we only had one arm, so it was perfectly balanced (we used the 2 extension springs in the kit in parallel & latex tubing to fine tune it). Can you believe we used a globe motor with a 1:1 gear ratio to move our 3' arm? Our arm only had a few positions to stay at so the LR ratio did not bite us. It did amplify how important LR ratio is, however; because our arm would resonate at other positions due to a 10:1 LR ratio.


: I why do we want a 1 to 1 ratio?

--- Think of a spring-mass system with 1 mass at each end and 3 springs in series connecting the masses. The 1st mass is your rotor inertia, the second mass is your load inertia. The 3 springs are you coupling, gearbox, and arm. More important than LR ratio is stiffness matching-find the least stiff member (usually the arm) and make it stiff!!!. Remember that you also have your controller "gain", which you want to make as high as possible. As you make it higher, the mechanical natural frequency has to be higher as well. Here is where the LR ratio comes in. We try to get it down to 1:1, but 2:1 is O.K.


: What good things does it do for us if we can get a 1 to 1 ratio?

Easy way to help control performance. The alternative is to use a low pass filter (I have an excellent 2 page article on it, but I will have to fax it to you). Actually, it is not necessary for FIRST robots, but is an outstanding way to eliminate vibration.

: Finally, does it make sense to add mass to the armature of the motor in order to improve the reflected inertia ratio? If I can get good things for the extra work, I may end up doing it.

Absolutely!! It is even easier than that. You just have to add mass which is rigidly connected to your motor. For example, if you attached a pinion to the motor shaft of the van door motor using a trantorque, then the inertia of the pinion and the trantorque could be considered part of the rotor inertia. The main drawback of adding mass to the rotor is the acceleration performance decreases due to the added inertia. On all of the robot arms I have engineered, the gear ratio needed to obtain a favorable LR ratio was always higher than the gear ratio needed for acceleration performance. Just something to chew on.

I apologize for being so winded, but you asked some detailed questions.

I hope you find this information useful,

-Paul

[archiver]

Posted by Joe Johnson at 04/26/2001 5:11 PM EST


Engineer on team #47, Chief Delphi, from Pontiac Central High School and Delphi Automotive Systems.


In Reply to: questions from a speed/torque guy...
Posted by Joe Johnson on 04/25/2001 7:04 PM EST:



Thank you for your response. It was great.

Of course, it only makes me have more questions, but
that is the way with learning isn't it?

It would be a great service to us all if you can pull
together a whitepaper on the topic.

Thanks again.

Joe J.

[archiver]

Posted by Paul Copioli at 04/26/2001 5:33 PM EST


Engineer on team #217, Team Macomb - Royal Fusion, from Utica Schools, Fraser Schools, Warren Cons. School and Ford Motor Company.


In Reply to: Excellent response...
Posted by Joe Johnson on 04/26/2001 5:11 PM EST:




: It would be a great service to us all if you can pull
: together a whitepaper on the topic.

Joe,

Will do. I will also include some general gear ratio stuff that a lot of people had questions about this year.

-Paul