SPFX Camera Dolly - Motor Acceleration Amps 1

[eckener]

Hi All... We are building a special effects film dolly. The motors have been sized and we are trying to estimate the current draw during the very fast accelerations... Doesn't seem to be too problematic for constant speed segments of our move profiles, but figuring out the current draw for accelerations has us a bit stumped.

Is there a relatively easy short-hand way to do this? perhaps using the torque constant (Kt)of the motor? or another formula that we have just been missing.

We have already figured out all our mechanical loads, wheel frictions, air drag forces, moments, gear- ratio, etc... We have this all in a spreadsheet where we plug in the acceleration rate and top speed. For simplicities sake, it spits out us a constant torque value on the motor shaft over that period of time to achieve that desired acceleration...

Now we want to find out how many amp hours that will approximately take.

We tried a couple motor sizing softwares, but they really didn't give us this information.

We did convert the whole shebang (including losses) into Work Done(Joules), then into Watts and then into Amps. When we compared that to the simple equation, Torque/Kt, the Torque/Kt was about 2-1/2 times higher... maybe this is because the voltage was not changing in this equation? Should we cut the voltage in half?

Its a brushless DC Servo motor (actually 4 of them.. Kollmorgen AKM series)
320Volt DC Battery Pack
Elmo Drivers
200 pound dolly with payload
3.91:1 gear reduction on motors.
6" diameter drivewheels.
27.4.mph top speed
14.65 ft/sec/sec accelerations (typical)

Thank you for reading.

 

[mikekilroy]

decided to just run a quick Motioneering on your movie cart using the data you gave above:

Its a brushless DC Servo motor (actually 4 of them.. Kollmorgen AKM series)
320Volt DC Battery Pack
200 pound dolly with payload (so 50# per motor)
3.91:1 gear reduction on motors (90% e3ff - easy to beat with any old planetary)
6" diameter drivewheels.
27.4.mph top speed (40/2ft/s)
14.65 ft/sec/sec accelerations (typical)

Your first pick AKM42J is a good one. I assumed a cycle of 0-6000rpm (27.4mph) in just over 2.5sec then decel to stop, wait 10 sec and repeat.

Your motors will each use 3.4nm for that 2.5sec accel (& decel unless you give some frictional info - but it will be minimal - I must use my brake to regen EVERY slight incline on the street in my car). This is 7.9 amps up to 320vdc, then 7.9 amps decel (regen) not counting friction. If my assumption is correct for your cycle of 1 move of 108.8 feet in 5 sec then stop for 10 sec then repeat forever, you will require 566 watts per cycle (regening 140.9 watts of that) per motor for a total of 2264 watts. So your battery usage will be 566 watts*15sec*4 or 566 watt-hours.. As your battery is 325vdc, and will likely droop to around 300v due to internal resistance (assuming you use about 6 amp hour cells - better plan on larger than you said above) you will pull about 7 amps avg from them if this cycle is correct as long as you run the cycle. Your peak amps draw from the batt pack when you are at 27.4mph will be 7.9a*4= 32amps. You will need to think about if average amps has any meaning to you: w/o thinking it thru it seems to me you need to consider rms amps not avg maybe. You had asked earlier if sine vs trap waveform effected the current calculations and I forgot to answer it: yes it does - the motors and drives will be rated in one or the other - they are about 1.6x different than each other since one is a sine wave and the other is basically on or off. So you need to know WHICH your motor Kt, Ic, & Ipk is rated in to make proper comparison if you do not just stick with a good sine drive and motor. Your inertia mismatch is about 89:1 which is probably fine for what you are doing. A good 6000rpm motor should be able to run at 0.1rpm smoothly. Hope this helps.

 

[mikekilroy]

forgot to post speed torque pic from Motioneering showing your rms and peak requirements superimposed on the motor curve...

 

[eckener]

Hi mike, I'll keep this real brief as I'm mid-road trip between LA and Seattle!

The link to the mavilor product manual is right below where the link to the two page thing you were looking at is. All the data for the 48 volt windings are there on page 17, and other voltages above.

The mavilor engineers told that these motors are so much faster mainly because of the slotless stators, a manufacturing technique that They explained is difficult and expensive so many of the larger motor vendors don't bother with it. I don't
know if this is true or not, but the numbers are the numbers and they are quite impressive.

Thanks for the calcs, I'm not looking at my spreadsheet right now but those numbers sound just about right. I do have all the numbers for the various wheel rolling friction forces (18 wheels under various loads) , the friction forces from the spring pressure of the drive wheels and the air drag resistance. I will post these later if you want

One item that did not match from you analysis however was the inertia ratio, which I had, and another application engineer at one of my vendors, at 58:1.

I had been wanted to get this inertia ratio down for two reasons, first because the system has a lot of compliance already with polyurethane coated drives heels and synchronous belts. In addition this is a repeatable system and should be able to maintain positional accuracy to within .15mm. That's why I was striving for the ideal of 10:1. ( though the closest I've gotten even with the mavilor is 24:1)

Again thanks for everyone's help on this, you and this forum have been really great

 

[mikekilroy]

'so much faster,' 'due to slotless stator,' what data on the spec sheet proves the 'so much faster' claim? faster can mean go higher rpm - nothing to do with stator design but mechanical limits of rotor design. faster can mean quicker acceleration so T=Jw/t calc - I don't see this as a case here for you either - consider.... with your much higher inertia load than motor, a fast accel low inertia motor gains YOU and your system nothing. I would be very interested in what their folks say makes it so much faster? perhaps we can look at their claim in a real engineering light?

on inertia mismatch, what do others say? higher? lower?

 

[eckener]

You offered to compare to other motor, which I greatly appreciate and have told where the spec sheet is a couple times as well as uploaded a curve here. You naysay it, but have you even run it through your calculation to see if your criticism is founded?

 

[mikekilroy]

i offered and did. posted jpg comparison of all relevant specs except inertia in my post 7 Aug 13 14:33. and no need to compare the inertias since they have little meaning to your project since your load inertia is so much higher than the motor anyway.

 

[mikekilroy]

bottom line is that fp motor picked is way undersized as shown and not capable of even doing the job. its specs are even lower than the equiv I compared it to. Hence my question why they say it is 'faster?' maybe some other spec I am not considering?

 

[eckener]

Hmm I dont know how you are calculating it. I do know that I have run it through the exact same calcs as the kollmorgens, that got similar results to your earlier post, and the numbers come in better on every level. I was extremely careful entering the motor data correctly. It does need to geared higher of course. I think I had it spinning at 8500rpm at 27mph.

It had more headroom on the peak torque, more headroom on the rms torque, lower inertia ratio by half, and using the fp0207.8 (48v winding) would go up to 18k rpm (or 57 mph) if I could find gears that would survive.

How is this way undersized in your opinion?

 

[mikekilroy]

There is no calculating to do.

Your curve shows SYSTEM PEAK limit of 2.2nm (red line) this is almost 4x smaller than you require for your accel spec.

Your curve shows CONTINUOUS of only 1.6nm (green line); this is most likely 2x smaller than you require for your cycle.

The motor peak of 12nm (about 160 amps!) is not achievable any longer due to the hi current it would require at 48v winding.

The 20,000rpm is not achievable due to the encoder 8,000rpm mechanical limit.

IF this motor could achieve 20,000rpm & 12nm, that is 33HP! Where would you find a 1 or 2" size drive to achieve this 25,000.00 watts to drive it?

These are the reasons I said this 48v winding motor is way undersized and will not do your application.

 

[eckener]

Hi mikekilroy....

Sorry I was out of commission for a bit...

So, regarding these Mavilor motors, I just don't see these motors being as underpowered as you make them out to be, even considering the current limited torque. To be sure, some are not as strong perhaps as the Kollmorgen (ie. the 48volt windings), but others definitely are, especially when you consider a higher gearing.

For example, take the case of the Mavilor FP0207.23 compared to the Kollmorgen AKM42J, both geared for a straight and level run at 27.4 mph. Attached is a both a pic and a spreadsheet of the results for a KM42J compared to an FP-0207.23 both of which have been run through the exact same calculations. The only difference in the two sets of inputs is the gear ratio, being 3.9:1 for the Kollmorgen and 5.5:1 for the FP0207.23. Geared thusly, the Mavilor just seems to beat the AKM in most every category, including weight, size, inertia ratio, and most of the margins for torque... also, it would appear to be more efficient on the batteries as well, and by a considerable margin.

Perhaps there is still something I am missing, but I am attached the spreadsheet and results for you to see and compare if you want.

P.S. Indeed the encoders cap out at 8000rpm, but the resolvers are good up to 20k rpm: this is confirmed and tested on the drivers we are considering. Resolvers are fine for our application.

 

[eckener]

...and the spreadsheet

 

[mikekilroy]

Hi Eckener,

Please don't think I disagree with your basic premise that those motors can have very high torque to weight ratios; I don't. I was just referring to the ONE 48v winding you thought could do more than it could. OK on resolver higher speed too (although I still don't see how you could USE it in a gearbox). Anyway, yes, what I saw were some very good motors. If I get a chance and you want another opinion, I will look at your comparison.

 

[mikekilroy]

Hi Eckener,

I added a column to the spreadsheet to include a more apples to apples comparison; you were comparing two different frame size motors (70mm vs 84mm). So the added column is the same square size motor.

I am not sure what criteria you feel is more important than others though so cannot comment on it being better or worse. Seems all 3 will do the job. The added motor is very similar (almost identical) to the FP model except it has much lower inertia and higher continuous torque. Often the figure of merit used to compare high performance of servo motors is torque to inertia ratio; the larger this ratio the faster the motor can accelerate. Again, in your case with a huge load inertia, this figure of merit is of little importance to you.

So by picking similar diameter motors with almost identical winding constants, the battery draw should almost the same. I would go for more Trms margin to let me run the motor cooler or increase accel of system if needed. I also would not go 8000rpm with mechanical gears. I added two comments to the top portion of your spreadsheet, correcting inertia units & other reminding that the internal regen capacity of the drive is probably of no importance to you either since all regen will simply go right back into the battery pack instead; my experience with similar LiFePO4 cells is they will pump up to about 3.5v @ same 30amp regen, so your bus with say 108 cells will pump up to around 380v max so never turn on the drive regen IGBT.

 

[eckener]

Thanks, Mike... I very much appreciate your reply. I'm a bit new to this level of engineering, so I welcome your double check.

It does look like all these motors will all do the job. With that said, the criteria I am really trying to juggle and weigh the options on is the gearing. The primary concerns are, as much as possible, making sure it is:
[ol 1]
[li]Vibration Free and[/li]
[li]Quiet.[/li]
[/ol]

On the one hand, the AKM42J has a "relatively low" 3.9:1 ratio, which I can do with a single synchronous belt drive, (Was thinking Gates GT2, 5mm pitch x 25mm wide). This keeps the large gear under 6" in diameter (which conveniently is just slightly smaller than the drive wheel) and simplifies construction. Whether the belt can handle 2500+ fps around a very small sprocket is something I need to look into.

On the other hand, anything above a 3.9:1 (the Mavilor, or the the other AKM you suggested) will either require a considerably larger drive sprocket, which just doesn't seem wise or compact, or a two stage reduction, possibly belt to helical gear.

If I can figure out a good gearing solution, I'd probably go with the Mavilor, as that does have the highest margins.

Regarding Regen... I just haven't quite got too into it yet, and need to do more research. I had those input parameters in there just to help size dynamic braking resistors for kicks. It was quite confusing, because every drive manufacturer seemed to have a completely method for calculating the power rating and resistance value of the resistor. In any case, it seemed that they were going to be quite large and hot, and not something I really wanted on the dolly, so yes, I do want to do the regen. I just don't know quite enough about it at this point to discuss intelligently.

 

[mikekilroy]

You seem to have your mind made up to use the Mavilor, so why not go larger frame? Next size up gets into the akm42 frame size; that lets you pick one similar in performance to the akd42. One or 2 more sizes larger gets even bigger allowing lower and lower timing belt gearing for quieter. You could even consider going large enough for direct drive for the quietest 'transmission.'

 

[eckener]

Good points... and I will definitely look at them, but first was trying to make sure my calculations were mostly correct. Its a bit frustrating however with those Mavilors, because since they don't have any sizing software or publish the torque curves, you have to send emails requesting individual torque curves. Maybe I don't need them, but otherwise I can't really tell what the top speed of the motor under a certain load would be.

I guess my concern about going bigger and slower is just the "resolution" as I call it, at low speeds. Most often, this dolly will work at very low speeds from mere inches per second to 1 foot per second. It is at these speeds that we will need the most amount of "smoothness" (really, it has to be "glass" smooth for camera work... definitely wouldn't want to see any cogging torque or anything like that)

Also at these lower speeds are where we would see the need for very accurate repeatability or "motion-control" style shooting. (this is a visual effects film term, not to be confused with the more general industrial term)

The AKM42J would be around 150 RPM at 1 foot per second... and and inertia ratio of 58:1

Now... maybe my fear is unfounded, and I would really like to find out that it is, because then I could gear much lower, go for slower motors, and even have one gearing that handles all speeds from a crawl up to 60 mph. That would be great.

 

[mikekilroy]

Echener, I do not want to hog the replies to your posts; I hope others pop in with comments also!

but first was trying to make sure my calculations were mostly correct.

Echener, You wonder if your motor sizing spreadsheet is accurate; I would remind you that you have been given a few different ones and you should compare yours to those. I did go thru one myself with Motioneering(tm) and it came out very close to another one posted. That said, I did not again go back and compare your latest xls data to it. But IIRC you show needing 0.9xnm Tc and the other 2 showed needing over 2.x nm - I will not go back and compare now after the fact, so if I am wrong, so sorry. But you DID ask. IF we show over 2 nm required and you show 0.9nm required, I would suggest your spreadsheet is not as accurate as it should be.

Maybe I don't need them, but otherwise I can't really tell what the top speed of the motor.


Of course you need each individual curve or you cannot logically pick the motor.

I guess my concern about going bigger and slower is just the "resolution"


I have these same size AKM motors on automotive VERY high performance cam and crankshaft racing engine grinders to 0.0001 or better accuracy.... grinding cams at 0.03rpm & 1/2 Tc rating, and yet rapid traversing at 4000rpm. Good servos are DESIGNED for this. You need to ASk your servo provider if they can do this function instead of guessing.

I would really like to find out that it is, because then I could gear much lower, go for slower motors, and even have one gearing that handles all speeds from a crawl up to 60 mph. That would be great.


I suggest you really need to team with an good servo application engineer on this if it really has to work the first time thru. These guys LIVE for helping you in this kind of application in exchange for selling a few of their products. IT IS usually FREE MAN! If you get a couple iterations of buying wrong hardware and spending time trying to make it work, then you can get away without it!

Such things are REGEN need addressing also; you haven't gotten into it enough yet to realize, but you must decide on how many LiFeP4 cells to use; with your potential regen requirement, this is not a no brainer; if you want to continue to say you will have 320v@30a, then you will have too high a voltage for ANY drive to control on regen. In this kind of application you MUST regen into the battery pack; yet you show voltages that are not consistent to do so.

Your Position controller is just as important to the final result; have you picked it? Delta Tau Kollmorgen built into the AKD drive Other?

 

[eckener]

_{Echener, I do not want to hog the replies to your posts; I hope others pop in with comments also!}

Hog Away... i will unabashedly gleam information from anyone who offers it. And please, don't feel compelled to reply just for my sake. I appreciate all the help you've already offered.

_{I suggest you really need to team with an good servo application engineer on this if it really has to work the first time thru.}

I can't argue with this point..... (hahaha) BUT.... there will be some time for R&D and so it doesn't absolutely have to work the first time, but there are so many other systems and design elements that will depend on the size and shape of the "powertrain", that it behooves us to figure out as much as possible beforehand. I do wish we could bring on an expert, but alas, this is the case in many areas of this project, and right now, we just have to figure out as much as possible on our own.

Your point to utilize the app engineers at the vendors and manufactures is a good one, and I actually have been, but up to this point none have really just come out and said to try going "big" with the motors to reduce the speeds. Rather they have kinda just gone along with my initial request for "really fast" motors and we've worked to get the inertia ratio down. Now, partly because of your comments, and partly because of the high decibel levels that I see will be produced by synchronous belts at those high speeds, I am really thinking hard about this strategy.

_{But IIRC you show needing 0.9xnm Tc and the other 2 showed needing over 2.x nm}

The first specs I posted with were for going up an incline... the later specs in the motor comparison were for level track.

_{I have these same size AKM motors on automotive VERY high performance cam and crankshaft racing engine grinders to 0.0001 or better accuracy.... grinding cams at 0.03rpm & 1/2 Tc rating, and yet rapid traversing at 4000rpm.}

This is good to hear. I did run the numbers for the Mavilors up to a 1:1 ratio: an FP0711 with a slightly smaller drive wheel pretty much does the trick... AND theoretecially it gets us all the way up to the top speed of 60mph, without having to offer a separate "high-speed geared" version of the rig.

It basically comes down to the choice between small and very fast motors (noisy)... or very big and slow motors (quiet).
If both can perform equally well at the low rpm, then increasingly, I think the choice has got to be the big and slow motors.

_{if you want to continue to say you will have 320v@30a, then you will have too high a voltage for ANY drive to control on regen....}
That spec is for a battery pack that is feeding 4 controllers, with the current based on the RMS torque of each motor.. so that's conservatively 6 to 7.5 amps for each controller.

_{you haven't gotten into it enough yet to realize, but you must decide on how many LiFeP4 cells to use; with your potential regen requirement, this is not a no brainer; i}

I suppose having more batteries for regen is because we theoretically could generate more power in braking than the 400-ish volts that the pack will be? Though I don't fully understand how we could generate more voltage, unless the rig were actually traveling faster than we could accelerate to in the first place. (higher current than we put into it? sure... but higher voltage?)

I do know that we'll need more cells just to provide the voltage at those high current levels. Right now I was looking at the A123 (bankrupt, yes) and K2 cells, . With the A123 we'd need around 116 cells just for the voltage drop due to current.

_{Your Position controller is just as important to the final result; have you picked it? Delta Tau Kollmorgen built into the AKD drive Other?}

Our favorite right now is the Elmo Gold Trombone. We like it because it is extremely small, (we'll have four onboard), is designed specificaly for DC input up to 400vdc or 800vdc, handles pretty high current ( up to 20 amps), has no noisy fans, and the milspec version has a very good heat rating (if it can be afforded). It can also be soldered directly to our custom driver boards. It doesn't handle regen or shunting directly, but neither does it preclude it as some other drives have done.

 

[mikekilroy]

glad to hear you are continuing to research all this - i bet you'll end up with a good system you are happy with in the end.

It may not be obvious in basic literature, but all decent gearbox mfgrs have db specs for their various boxes so you can compare.

I can see most servo suppliers not suggesting lower ratios; they will generally accept your given criteria and not suggest very far off other ideas as they don't have time for it often, and a lot of engineers are quite hung up on that darn inertia match number and will have blinders on regarding straying far from it.

Since you are considering other ideas, there is also this newer concept called 'direct drive.' It leaves inertia matching as an cave age idea, no longer important at all. Makes for the quietest and probably smoothest velocity also. I apologize for only knowing 1 good source to point you at to see the concept, but I am sure you can google others after you get the gist of it here:

http://www.kollmorgen.com/en-us/products/motors/direct-drive/housed-d-and-dh/housed-d-dh/

 

[mikekilroy]

I forgot to include a suggestion on your 116 cells also; I think this is 8-16 MORE than you want or you will never regen into the batteries to help recharge on decels, and you WILL need those big hot resistors.