

03182009, 03:42 PM

#91

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Join Date: Mar 2009
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Posts: 139

I understand the error as follows:
% error = ((theoretical  actual)/actual)*100
I put the theoretical model wT as the error. I put your predicted speed wP as the "actual", i.e., measured, value.



03182009, 11:08 PM

#92

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Join Date: Mar 2009
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John,
I confirmed what you say about getting the same maximum power of 216 Watts with a few data points near the peak power value to my satisfaction.
I make a text file of your predicted velocity data on the interval:
1.0 874.12
1.1 940.89
1.2 1004.31
1.3 1064.53
1.4 1121.69
1.5 1175.91
1.6 1227.33
1.7 1276.09
1.8 1322.30
1.9 1366.08
2.0 1407.57
and read this into a Numerit Pro array of time and speed, take the array derivative of speed versus time (which claims to use a cubic spline method) to get angular acceleration, multiply by system inertia J to get torque in the flywheel, then multiply by the speed and I get back 215.8 Watts peak power.
Last edited by SystemTheory; 03182009 at 11:17 PM.
Reason: more clarity



03192009, 10:53 AM

#93

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Join Date: Aug 2002
Location: Houston, Texas
Posts: 3,777

Good. We had some trouble with a cubic on the wider set of data. A fourth order model was better suited. I imagine this cubic spline is fitting a cubic model to smooth the data. Not sure on that.
John



03192009, 11:54 AM

#94

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Join Date: Mar 2009
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Posts: 139

John, I am refreshing my memory on some of the established numerical methods for statistical analysis and curve fitting at this time. It has been a while since I applied any of it directly.
I did notice, however, that when I first tried to calculate the starting rate of acceleration at the axle of a T2 Car using the velocity curve published in Xtreme RC Cars magazine, my first approach was to build a theoretical curve:
v = vmax*(1  e^(time/tau))
where v is velocity, vmax is the maximum published velocity, e is the natural logarithm, time is continous from 0 to the maximum acceleration time tmax, and the time constant for the system is tau = tmax/5.
I quickly found out perhaps a dozen limitations within this approach, but I learned a lot. One thing I learned was that the "aderiv (v , t)" command in Numerit Pro does not always give back an accurate rate of starting acceleration compared to taking the derivative by hand. However it is pretty close to the theoretical curve in all but the starting rate of acceleration, and it is accurate in some cases.
The main error was right at the zero velocity point, where acceleration is proportional to stall torque in the motor. Thus the numerical error in addition to other problems with this "reverse engineering" problem were exposed.
Since then I have found that integration is generally much more reliable in various engineering computer tools than differentiation. Therefore I prefer to integrate when I set up theoretical models. The way I understand this, the integral is a smoothing function and behaves better at sharp boundaries in the data.
In the Sentry Dyno there is no choice but to take the derivative using a speed sensor. My only concern is that this introduces the question of error when taking the numerical derivative, and since this is an Open Source effort, some analysis and description of that error would be appropriate.
I'm posting up a PDF on the basics of statistical methods for reference. I found it "as is," no author, no source information. It is 7 pages and I'm personally finding it useful to refresh my memory on the chain of reasoning in specifying error during a measurement / calculation process, so I hope other visitors find it useful. The treatment of "Propogation Error" can be applied here, for example, in the calculation of flywheel inertia. The same concept must be extended to the methods we use to calculate the data in a spreadsheet, so that when we measure 216 Watts at 1150 rpm, for example, we know that there is some error in each number that is acceptible for our purposes.
I think a lot of controversy over Dyno data is caused by the fact that the hardware specification and software calculation process is not Open Source, so people go round and round debating the numbers.



03192009, 12:20 PM

#95

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Join Date: Aug 2002
Location: Houston, Texas
Posts: 3,777

"In the Sentry Dyno there is no choice but to take the derivative using a speed sensor. My only concern is that this introduces the question of error when taking the numerical derivative, and since this is an Open Source effort, some analysis and description of that error would be appropriate."
We have an equation describing Angular acceleration. There is no error taking the derivative and from this point until the end of our spreadsheet as we are only doing mathematical operations. The way you would describe the error when ever you do mathematical modeling is by plotting the 95% confidence levels. In excel if instead of using Linest which only gives the parameters of the model ,you use the regression function. Then you get the parameters of the model and the parameters for the 95% confidence bands (equations) which can be plotted above and below the model. With 95% confidence you can predict that actual power numbers are between these bands. Be glad to this later. Please continue by PM. The Novak Sentry project is finished to my satisfaction. No confidence bands are needed. We have Fantom runs to correlate with it.
John



03212009, 02:33 PM

#96

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Location: Houston, Texas
Posts: 3,777

Error and Confidence Bands
I had a nice discussion by PM with Charlie Suangka who was the head tech or the face of Novak for many years. (He is no longer at Novak). We had conversed previously a good year ago and shortly afterward the light motor series from Novak was made. He has experimented quite a bit with the Novak Sentry and had good confidence in the RPM values that were produced. He agreed the first few points of our dyno run had reached the limit of the amp range of about 108 amps and this was causing errors in those first few reading.
The graphs below give us just one handle on the error in RPM.
The blue squares show the Angular velocity (like RPM) plotted with respect to time. If you look closely at the first three blue boxes on the left you can see that they are jumping around a bit. The amps are pegged in the Novak and it is acting a little erratic. Then things smooth out. If you look even closer again you can see a very slight wavy nature to a line formed by the blue boxes. This has to do with the RPM selection from a chart rather than being a direct measure. Occasionally you will be high, the wave goes up,then you will read low. This also has to do with having only one port for the sensor. Occassionaly that hole has just past the sensor at a reading, the RPM may be a little high, and then the hole is just short of the sensor the RPM is a little low. This waviness is less than 1% and is not significant because we smooth it out with the spreadsheet.
Behind the blue boxes (the experimental data points) is a black line. This is the line of predicted velocity for the flywheel. It is as good as you are going to get. The line cuts right through the middle of most boxes. The correlation coefficient R is 0.999792786. The closer to 1 the better the model fit the data. It's pretty close;the model fits very well. But then there is that mess at the very beginning. That mess at the beginning creates a lack of confidence in all the data if that were our only source to trust these values.
The red and yellow lines give us a confidence band. With 95% confidence we can say the true RPM lies within these two bands. Notice the band gets quite big at a high number of seconds. Up to about 2 seconds our band is narrow and error is manageable, over 2 seconds things are not looking so good.
Now I just take my best guess for RPM on point 24. That's where most of our error estimate comes from. I get the second plot on the right. I have improved things all the way to about 3 seconds then the lines spread again.
That is the pure statistical approach with no other data but this RPM sensor on hand.
Now we will throw in some more things to see if we can create more confidence in the blue line. One thing we can do is use the Kv (the RPM/volt published for the motor) of the motor to see if high RPMs are close. I think they would be. Another is we can look at hundreds of motor curves and see that they are all shaped like the blue line and not like the yellow or red line. That gives us more confidence in the blue boxes. I have all the confidence I need when I see that black line cut through the middle of blue boxes, and when I talk to Charlie and he aggrees the RPM should be pretty accurate except for the readings at 108 amps or higher.
Relative Standard Deviation
Another handle on error is to calculate the Relative Standard Deviation that the PDF above talks about. To do this you need at least 3 max power runs done in as controled a manner as possible. This is the plus or minus ( +) at the end of a number, but this only tells you the precision of the measure (how close to each other the numbers will tend to be) rather than its absolute accuracy (how close to the truth the numbers are.
These two graphs result from a bit more complex version of the Novak Dyno calc spreadsheet. Ask for the Confidence Band Spreadsheet, [email protected]
Comparison to other sources of RPM
For the second to last data point in the set I calculate a Kv of 2656 RPM per Volt. This gives us about 12 % error over the Hacker published 2360 RPM/V. Given their huge power number at 315 W vs a believable 215 W (at 7.4 V nominal) from having run and dynoed many motors, I would probably use our RPM as the Theorectical value.
John
Last edited by John Stranahan; 03212009 at 03:37 PM.



03212009, 11:15 PM

#97

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Location: St. Louis, MO
Posts: 904

Charlie's gone?????????????? Where did he go?



03222009, 05:33 AM

#98

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Join Date: Mar 2009
Location: Metro New York
Posts: 139

John, thanks for the error analysis in the curve fit model. I see the statisitical fit is very good and confidence bands very close around peak power for the Hacker.
The current sensor appears to be a halleffect device. If so it probably is not limiting the current into the motor at all. For example the Allegro 754 sensor is accurate to 100A over a 5V linear output with only 100 microOhms series resistance in the sense path, and it can overcurrent substantially. This means it could flow 200A without distortion, but the sensed output will hit the 5V rail at 108 Amps (probably depending on a temperature derating) per your discussion above.
If you can pull the chip number from the current sensor, I would look for the exact specification. It may be possible to replace the sensor with a better range (200A +/ ?) if you can determine the voltage input level to the Sentry.
If you want to study the principles of hall sensor operation, here is one supplier.
Allegro's current sensor matrix:
http://www.allegromicro.com/en/Produ...rentsensor.asp
Allegro's 754 page with the specification in a link to PDF at the top right:
http://www.allegromicro.com/en/Produ...0754/index.asp
I mention this to suggest the hiccup on the rpm sensor may have nothing to do with the current sensor, if my hunch is correct. This would be good, since if the rpm sensor is accurate in the range of peak power chances are the motor is making its best power since it can draw all the current it requires from the very start. However the measured current value would be clipped at the amplifier output inside the halleffect sensor, if I am correct.
Also if the Sentry is reading the current on a 5V linear scale (or some other reference voltage level for analog to digital conversion) then it might be possible to fit a 200A hall sensor to the Sentry for high current sensing, although resolution would go down to probably +/ 1A.



03222009, 07:44 AM

#99

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Join Date: Mar 2009
Location: Metro New York
Posts: 139

The local AMA club is having a fun fly today. So I'm going over to see their field (it's atop the grass cap to the old landfill) ... maybe I'll join up.
This link includes some very useful concepts of intrument limitation error (ILE), propogation error in calculations, and a graph showing 95% confidence bands in the distribution curve, explaining what it means.
http://www.rit.edu/cos/uphysics/unce...rt1.html#range
The first thing I would consider in a flywheel Dyno is look at the instrument limitations and propogation error associated with the measurement of mass m and diameter D of the rotor/flywheel combination, then apply the power rule for propogation of error to specify a tolerance. Next I would try to identify the ILE in the rpm sensor.
Next there may be a resolution inside the Sentry for the analog to digital converter (ADC, 8 bits, 10 bits, 12 bits, etc) and this might reduce the resolution from an rpm or current signal presented in volts. I am assuming an ADC in the Sentry absent better information, since this would make the most sense.
Anyway just throwing out some information to help the community explore an Open Source type of project ... where the uncertainy in the numbers can be evaluated by the dilligent observer without sparking too much controversy on the matter. If it is not worth the extra effort that's OK with me too, since a good repeatable Dyno procedure obviously works for many individuals, and that's what counts most to some.



03222009, 01:49 PM

#100

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Join Date: Aug 2002
Location: Houston, Texas
Posts: 3,777

System TheoryThanks for the discussion. The upgraded sensor sounds interesting. I don't have the beast to tinker with though. I am looking for the 19 turn data you requested at the moment. I have the Fantom file located.
"The current sensor appears to be a halleffect device. If so it probably is not limiting the current into the motor at all."
Yes the motor amp limit is from the motor, battery, speed control, themselves. The sentry is what is pegged above 108 amp.
If you take 10 $100 temp guns and take a reading you will get 10 different values. It has to do with the continuous type of response and the variance in cheaper electronics. They may vary as much as 1012 degrees. Not that good. I have a suspicion that if you take 10 $100 RPM meters for airplane props and measure the RPM of the running engine with the proper light and cranked up to a stable RPM that you will get the same measure on all. The reason is that the measure of time is well established and accurate with inexpensive quarts clocks. The ability to count is also well established with the use of computer like circuits. It is more of a digital type of response. I predict there is little RPM or time error to found here on the Novak. If I were building and marketing a dyno from scratch then we would test our machine back to back with a good tach. We are not.
SteveLCharlie left Novak on friendly terms. He just moved away from the plant.
john



03222009, 05:11 PM

#101

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Join Date: Mar 2009
Location: Metro New York
Posts: 139

John,
I agree the rpm sensor is probably robust on the Sentry. As I was driving today I figured it should be a digital input to a counter, divided by a timebase derived from the microcontroller clock. Avoiding D/A and then A/D conversion makes more sense.
I understand an estimate of Kv (k, in standard SI) taken from the flywheel speed and battery voltage on the Dyno will be an approximation, with error on the low side, due to the presence of bearing friction. When you test for Kv in generator mode and measure output voltage on a voltmeter, you should get the ideal value for the regulated rpm and magnet temperature (and commutator conditions in the brush motor, electronic commutation algorithm in the brushless). It might even make up 12% for a cold motor.
I looked in a MATLAB book today and found two examples of curve fitting, to a line y = mx + b and to an exponential curve y = a*e^(b*x). I am wondering if your confidence bands might tighten up along the whole range for a fit to an exponential function in Excel?
I think the proper equation for fitting angular velocity is:
y = a*(1e^(time/b))
but I'm not sure how this applies in Excel at this time. I may tinker with it a little tonight.
It appears the free application R is now common in statistical education and numerical computing, and it runs on most operating systems. However I'll need to locate a good introductory text book before I test it out.
Last edited by SystemTheory; 03222009 at 06:09 PM.
Reason: correct equation



03222009, 08:39 PM

#102

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Join Date: Aug 2002
Location: Houston, Texas
Posts: 3,777

"I understand an estimate of Kv (k, in standard SI) taken from the flywheel speed and battery voltage on the Dyno will be an approximation, with error on the low side, due to the presence of bearing friction. When you test for Kv in generator mode and measure output voltage on a voltmeter, you should get the ideal value for the regulated rpm and magnet temperature (and commutator conditions in the brush motor, electronic commutation algorithm in the brushless). It might even make up 12% for a cold motor."
Interestingly in spite of air friction on the flywheel which is probably the biggest load up at speed my Kv value is higher than that reported by Hacker.
I am glad the "heat" is off the RPM reading. Measuring RPM seems like a simple task to me at this day and time. My first $7.00 full size car tach was probably not so accurate. It contained no digital electronics. The accuracy here was like the temp gun and controlled by buying more precise electronics the $250 Sun Tach. My $7.00 tach suted all my purposes though. The 300 H.P., 302 V8 was revved time and again to 7000 rpm without failure. After all we are just having fun here not doing billion dollar research or million dollar racing.
Although we could develop a theoretical base model and fit it to the data to improve our knowlege of the coefficients in the theoretical model, It will not improve our dyno. The black line goes right through the middle of the blue squares. You can't do better than this. The only way to do better is to cure the hiccup and waviness of the RPM data. Right now they are both at a very tolerable level.
John



03232009, 09:54 AM

#103

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Join Date: Mar 2009
Location: Metro New York
Posts: 139

John,
True, the air resistance on the flywheel may be the "dominant" velocity feedback at high rpm, and it would skew measured data from an exponential curve fit. The polynomial fit may indeed pick up this effect.
My initial logic confused Kv as being proportional to the SI factor k, where in fact they are inversely proportional. I always think in terms of k so power is in watts in both the motor circuit and mechanical system without any UCFs.
Customary Units
Kv{rpm/V} voltage constant
Kt{?/A} torque constant
UCF unit conversion factor (conservation of power in air gap)
SI Units
k{Vs/rad} air gap constant kV = kT = k, {Vs/rad} or {Nm/A}
Angular SPEED UCF
1 {RPM} = 1.0472E01{radian/s}
Case A:
Higher(measured) Kv:
Kv = 2656{RPM/V}*1.0472E01 = 278.1363{rad/Vs}
Lower (measured) k:
k = 1/Kv = 3.5953E03{Vs/rad}
Case B:
Lower (Published) Kv:
Kv = 2360{RPM/V}*1.0472E01 = 247.1392{rad/Vs}
Higher (Published) k:
k = 1/Kv = 4.0463E03 {Vs/rad}
ESTIMATED k:
My earlier very rough estimate k = 3.319E03{Vs/rad} may appear in a post above from an effort to "reverse engineer" the motor parameters from Dyno data. That gives back Kv = 2877{rpm/V} per my very rough estimate.
Best Measurment of Kv = 1/k:
The most reliable way to measure Kv or k would appear to be the open circuit generator test, since error due to friction and electrical losses is eliminated as I understand it.
Last edited by SystemTheory; 03232009 at 12:00 PM.
Reason: include figure 2877{rpm/V}; add generator test comment



03242009, 12:19 PM

#104

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Join Date: Mar 2009
Location: Metro New York
Posts: 139

I attach "simulated Dyno" time curves for a 19T stock motor.
Data adapted from Xtreme RC Cars Issue #136, Xray T2 '007 test.
Look online in the Performance Test Archives for the PDF.
The online PDF report is currently published here:
http://www.rc411.com/pages/reviews.php?review=55&page=3
The input block to my engineering simulator looks like this:
:PMDC Motor Input Data in Standard SI Units 
Vs = 8.2; ::[V] source voltage
Vnom = 5.0; ::[V] nominal input voltage
Ts = 148m; ::[Nm] nominal stall torque
wmax = 1974; ::[rad/s] nominal maximum speed
Jm = 3.12E06; ::[kgm^2] rotor inertia
JL = 4.1E05; ::[kgm^2] direct load inertia
tF = 2; ::[s] final time
J = Jm+JL; :total inertia
Nominal values are as published for the Fantom Dyno at 5{V}. Except I had to bump nominal stall torque Ts up from 99{mNm} to 148{mNm} to keep the maximum power at the published value.
In this simplified model the torquespeed curve scales by the factor Vs/Vnom. Results are shown in the attached graphs.



03292009, 05:01 PM

#105

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Join Date: Jun 2006
Posts: 872

Just so everyone knows, this project is not dead. I have been working with several identical dyno run setups and trying to come up with a standard way to conduct a test. This is my #1 goal right now. For instance, there is a slight hiccup with the Sentry at startup where it may record the RPM slightly off. So to combat this, these readings need to be deleted. However, do not worry. The mathematical model we are using predicts these deleted values based on the trend of the RPM curve vs. Time. The max torque is also predicted, however should be quite accurate since my flywheel is so heavy and takes at least 8 seconds for the motor to spin up to full speed we have a lot of data points to calculate off of.
Also, if you plan to do this on your own, the battery you use will affect the outcome, and probably no two Sentry dynos will be alike. That is unless a power supply is used that is around 7.2V and can supply at least 100A. Something like this could be expensive. My newest battery I am going to be using is a Reedy 35C 5100mah lipo. This should help keep the voltages more constant throughout the run, but it will of course make the max torque and max power a little higher too.
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