Accelerating Torque Calculation Dilemna 1

[nightfox1925]

As per IEEE Std. 399-1997 (Brown Book), under motor starting studies, the starting time can be computed using

t(sec) = Wk^2 (RPM1 -RPM2)/ (308Tn) ------at page 249

where Tn is the net average accelerating torque between RPM1 and RPM2. The motor WK^2 is assumed to be 270lb-ft^2
and the load Wk^2 is assumed to be 810lb-ft^2. Motor is 1800RPM and the book uses curve as indicated in Figure 9-3. A tabulation was made (table 9-3 page 258) to indicate the % torque of both motor and load at different %speed periods and the average net acceleration torque is indicated using speed-torque charateristics in Figure 9-3. I understand how %T(net) was taken but what confuses me how did they get the net acceleration torque in lbs-ft^2 based from the graph at different % speed periods. I am hoping some of you have a copy of this brown book. I may have missed something and I am hoping to get assistance. Thanks

GO PLACIDLY, AMIDST THE NOISE AND HASTE-Desiderata

 

[7anoter4]

hi nightfox1925
Acceleration time for electric motors is directly proportional to total inertia and inversely proportional to the electric motor torque. For electric motors with constant acceleration torque, acceleration time is: t=WK^2*(N2-N1)/308/Tacc
Explanation:
JM=motor inertia moment JL= load inertia moment
t12=(JM+JL)*2*PI/60* N/Tacc
t12=wk^2/g*(N2-N1)/60/Tacc*2*pi
t12=wk^2*(N2-N1)/Tacc/k
As J [moment of inertia]=WK^2/g g=acceleration of gravity =32.17 ft/sec^2; k=g*60/2/pi=307.24=approx.308
tstart=wk^2*(?max -0)/Tacc/308 tstart=total start time from standstill to ?max
Tfl = Php. 5,252 / ?max Php=Motor rated power [HP]
?max= Motor rated speed [rpm]
Net acceleration torque for a speed S is:Tacc=TM-TL[ this would be slight variable with S but we should state it is constant]
Average motor torque may beTMav= 0.45*(break-down torque+locked rotor torque)
Average load torque may beTLav= Tfl/3 [for a fan type load, for instance]
Average Tacc=TMav-Tlav and we say it is constant from speed=0 up to speed= ?max.
I hope this explanation will help.
Best Regards

 

[7anoter4]

hi nightfox1925
I have only an old edition [IEEE-399/1990] and the number of pages and the figures is a little different but finally I got your example. This is figured in the table:
Table
Average Value for Accelerating
Torque Over Time Interval
Defined by a Speed Change
speed Tmotor% Tload% Tnet% Tnet[lb-ft]=Tnet%*Tfl/100
0 100.0% 30.0%
---------------------------- 77.5% 2260.4
0.25 120.0% 35.0%
---------------------------- 100.0% 2916.7
0.5 160.0% 45.0%
---------------------------- 120.0% 2500 wrong!
0.75 190.0% 65.0%
---------------------------- 62.5% 1822.9
0.95 80.0% 80.0%

Tfl[Full Load Torque]= Php 5,250 / ?max
2916.667 lb-ft
Actually the table is as follows:
speed Tmotor% Tload% Tnet% Tnet[lb-ft]
0 100.0% 30.0% 70.0% 2041.7
0.125 110.0% 32.5% 77.5% 2260.4
0.25 120.0% 35.0% 85.0% 2479.2
0.375 140.0% 40.0% 100.0% 2916.7
0.5 160.0% 45.0% 115.0% 3354.2
0.625 175.0% 55.0% 120.0% 3500.0
0.75 190.0% 65.0% 125.0% 3645.8
0.875 135.0% 72.5% 62.5% 1822.9
0.95 80.0% 80.0% 0.0% 0.0
As you may see speed 0.125=(0.25+0)/2
Also Tmotor 110%=(120%+100%)/2
Tload 32.5%=(35%+30%)/2
Tnet%=Tmotor%-Tload%
Tnet[lb-ft]=Tnet%*Tfl/100
Best Regards

 

[nightfox1925]

Thanks Zanoter for your support. I am looking into it at the moment.

 

[israelkk]

What about the Back EMF? There is no constant acceleration in real life. You have to use the motor complete differential equation to solve the current build too. The L * dI/dt and Ke * Omega must not be ignored.

 

[7anoter4]

Hi israelkk
First of all thank you for your remarks.
The transient phenomena in starting motor may be divided in a few steps:
1. Subtransient period [milliseconds duration].
In these case, of course ,you need Ldi/dt and E calculation.To study these phenomena one needs Laplace Transformation help.Neverthe less is a very ineresting field usually is neglected due to complexity and very doubtable results.Even for shortcircuit calculations only the transient is taken into consideration.
2. The transient period theoretically may be calculated using Steinmetz model.Steimetz model study the phenomenon as harmonic[in comlpex calculation] only.
There are still a lot of problems: the parameters[r,x] are not stated accuratelly due saturation of iron[mainly on the stator and rotor teeth] and other phenomena as skin effect of rotor bar from rotor slots. So all these return the parameter nonlinear. The superior harmonics are also neglected.
In so far for transient current only manufacturer data may be used.
The simplified equations as per IEEE 399 is fair accurate since all the motor data produced by manufacturer have an error of 15-20%.[The torque values I mean]
The above table, extracted from this standard, is based only on mechanical calculation, it is not an electrical transients calculation.
There is only an example [I think, may be an induction motor –class B as per NEMA MG1-actuating a blower ,a fan or centrifugal pump] so the net acceleration torque is fair constant.
Best Regards

 

[israelkk]

I am in the aerospace field. I have seen many bad designed systems where the electrical and the control guys ignored those transients and after four years of development they have found that the moving aerodynamic surfaces moved too slow or even failed to reach the aerodynamic loads.

A more accurate analysis clearly showed that what received in the tests is what was supposed to happen. If the analysis was correctly done without shortcuts a lot of money and time could be saved.

Laplace analysis is not the only way to go. I write the system differential equations including the motor constants, resistance, inductance, aerodynamic loads, inertia, etc. Next I numerically solve the system of equations for loads and movement with time.

99.99% of the time I use Mathcad which is more than enough. It is usually a short spreadsheet and once you have done it it can be reused with minimal changes if any for other systems and cases.

 

[Skogsgurra]

Hello 7another4 and israelkk!

I think that israel needs to understand that this is not a DC motor. Your remarks about EMF and such things indicates that you think it is.

The variable torque of an induction motor is somewhat different and the approximations shown by 'another' are reasonably correct. If you need better, you have to simulate or do a real-thing test.



Gunnar Englund

http://www.gke.org

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100 % recycled posting: Electrons, ideas, finger-tips have been used over and over again...