Acceleration time
Acceleration time
(OP)
Hello All
I have bit of a problem
I have two torque speed curves, one showing the motor torque the other load torque. But I need to find the Acceleration time; I have the true torque values along each line in n-m and the speed in rad/s. In addition I have the kW rating of the motor. But I do not have any other data.
Is it possible to find the Acceleration time, or an approximation for it.
Help would be much appreciated
I have bit of a problem
I have two torque speed curves, one showing the motor torque the other load torque. But I need to find the Acceleration time; I have the true torque values along each line in n-m and the speed in rad/s. In addition I have the kW rating of the motor. But I do not have any other data.
Is it possible to find the Acceleration time, or an approximation for it.
Help would be much appreciated





RE: Acceleration time
RE: Acceleration time
Let's say you have motor torque Telec(w) and load torque Tmech(w)
J = total inertia
w = radian speed
accelerating time = t
t = J*Integral{1 / [Telec(w)-Tmech(w)]} dw from w=0 to 2*Pi*finalspeed.
RE: Acceleration time
Tm - Tl = J á
(this is analogous to force = mass x acceleration used in linear motion calcs)
where
Tm = motor shaft torque (Nm)
Tl = load torque (Nm)
á = angular acceleration (rad/s^2)
J = total moment of inertia (kg m^2)
In other words, plot a graph showing (Tm - Tl)/J against speed and this curve is the angular acceleration.
The difficult bit is finding the total inertia - this has to include every rotating part i.e. the motor rotor, shaft, load (referred through a gearbox if there is one). It can however be calculated by simply adding together the inertias of all the individual components. Probably the most useful equation is the m of i of a solid cylinder:
J = 0.5 M r
where
M = the total mass of the cylinder (kg)= density x volume
r = radius (m)
RE: Acceleration time
Why integrate between 0 and 2*pi*final speed ,and not just the 0 – final speed
RE: Acceleration time
RE: Acceleration time
I still think it will be sensible to estimate the inertia by calculation rather than by any rule of thumb (which I'm not aware of), provided you can see the approximate dimensions of the rotating components.
electricpete - what if the motor and load torque vary with speed? if they do, you will need an expression of torque as a function of speed that can be integrated, that's why I started looking at the graphical approach.
RE: Acceleration time
Taccel = J*dw/dt
dt = (J/Taccel)dw
Integrate both sides to give the equation above.
w=radian speed = 2*pi*rotational speed
that is where the 2*pi comes from
As far as estimating inertia's:
1 - Motor - NEMA MG-1 has a formula for estimating motor rotor inertia for the purposes of dynamic braking calculations.
Motor WK^2=0.02*2^(poles/2)*hp^(1.35-0.05*poles/2)
2 - Load - NEMA MG-1 identifies the MAXimum load inertia that can be started by a standard induction motor is
Load WK2 =+A*hp^0.95/(rpm/1000)^2.4 - 0.0685 *hp^1.5/(rpm/1000)^1.8. BUT, YOUR ACTUAL INERTIA MAY BE FAR LESS THAN THE MAX.
For both the motor and the load you can estimate from the geometry of the rotors - dimensions and density. I would trust the motor estimate above as a reasonable alternative to the geometric approach, but be very careful about that load formula which is a MAXIMUM.
RE: Acceleration time
Couple of questions on electricpete suggestion:
1.In the load estimation equation what is the +A?
2. Do the inertia estimation equations still work if I convert to SI units ie rad/sec and watts, instead of RPM and HP
3. The 2*pi*rotational speed integration, do you still need to do that if your speed is in rad/sec.
RE: Acceleration time
I forgot to mention that these formula's are all in American/British units.... inertia in lb-ft^2, power in horsepower, speed in rpm
RE: Acceleration time
RE: Acceleration time
your help was much appreciated
RE: Acceleration time
RE: Acceleration time
Also if driving a pump, the interaction of impeller and fluid decellerating at unknown rate from fluid friction (I'm pictuing a closed fluid system) seems unpredictable.
RE: Acceleration time
First, let me say the I can't understand why such parameters aren't known for a motor (and driven-machine) of this size. It is relatively inexpensive to determine the motor's moment of inertia during factory test!
That said, then for academic purposes, the following will determine the rotating moment of inertia.
At time t=0, turn power off. Then the moment of inertia can be determined from the speed decrement, by plotting N (speed) with respect to T (time). The slope, dN/dT, at t=o will be proportional to the total moment of inertia, i.e., motor plus driven-machine. Of course a torque value will be required. At t=0, the motor torque will also be zero, so one can use the torque of the driven machine, at the time power was removed. Or, one can determine the average driven-machine torque taken from the manufacturer's data.
Now there is a downside to the above. That is, it will be difficult to obtain dN/dT at t=0. For greater accuracy, measure the slope at several points along the decreasing curve and plot dN/dT with respect to t. Then extrapolate the resultant curve back to t=o.
If you want the math, let me know!
RE: Acceleration time
The test procedure noted earlier, of course, requires a running machine, in which case the Wk^2 calculation is obviously redundant!
If you need a preliminay, but fair, aproximation for the motor, it is:
Wk^2 = (K)x(D^4)x(L), where:
o Wk^2 = Moment of Inertia, lb(f)-ft^2.
o D = Rotor Diameter, inches.
o L = Rotor Length, inches.
o K = Factor for steel construction = 1.92E-04.
RE: Acceleration time
RE: Acceleration time
I was intrigued/interested in shortstub's suggestion of a way to determine inertia using coast-down data, since I have never heard of that. It's an interesting idea and I'd like to explore it more (although it's not related to the original post).
Here is my model to analyse the situation.
We have inertia and friction in the pump. (I include the whole rotating assembly inertia here)
We have inertia and friction in the fluid.
IF we assume for the moment that there was no interaction between the pump and the fluid, then each of them would have a velocity decreasing as v(t)=v0*exp(-t*friction/inertia). (I use the term velocity loosely… it refers to rotation of the pump and linear motion of the fluid… there presumed a known conversion factor between pump rotation speed and fluid linear motion speed which is not important to the discussion.)
Of course the assumption that there is no interaction is not correct, and the actual interaction will force both the pump and fluid speeds to decrease together. Whichever one would tend to decrease speed faster will absorb energy from the one that tends to decrease speed slower, so that both speeds decrease together.
But the comparison of the time constants of the pump and the fluid tell us WHICH DIRECTION the energy is transferred by that interaction. Specifically:
IF the fluid has a faster decay constant than the pump, then the interaction will transfer energy from the pump to the fluid during coastdown. This might be a good approximation for a fan with high inertia pump air with low inertia. In this case (if we also neglect pump friction), then the decellerating torque is in fact very similar to the fan torque. (the fan can't tell the difference whether it is being driven by motor torque or by torque associated with very slow deceleration of a very large inertia).
BUT, IF the pump has a faster decay constant than the fluid, then the interaction will transfer energy from the fluid to the pump during coastdown. I believe this will be the case for a high-velocity/low dp single-stage pump pumping water through a closed-loop system. In this case the initial (prior to deenergization) pump torque has no relation whatsoever to the decellerating torque. In fact the direction of the torque associated with interaction between pump and fluid is in the direction of acceleration… it is only the friction of the pump which is causing the decelleration.
I think the latter case may be an extreme case. But it illustrates the error of assuming that the decelerating torque is the same as the pre-deenergization pump torque in cases where fluid inertia is not negligible (compared to pump inertia) and to a lesser extent when pump friction is not negligible (compared to fluid friction). This is probably a negligible error for fans (high rotating inertia, low fluid inertia), but a bigger error for pumps.
I am not criticizing the suggestion, just discussing it. Interested to see if others agree with the above.
RE: Acceleration time
"Control of Electrical Drives", by Leonhard.
RE: Acceleration time
Here is another idea you may want to use to determine a preliminary value for GD^2:
Throughout my career I collected machine parameters. One set of data involved uncoupled runup times of large motors.
If your 10,000 kW (13,600 hp) motor is 2-pole, 3000 rpm, then the time to accelerate to normal operating speed is about 3sec, +/- 10%.
Thus, you can now use the normal torque formula and solve for GD^2:
GD^2 = 375x(Ta)x(Tm)/(Nd), where:
o GD^2 = motor Moment of Inertia, kg(f)-mt^2.
o Ta = runup time, seconds.
o Tm = motor torque, kg(f)-mt.
o Nd = rated speed of motor, rpm.
RE: Acceleration time
1. HP induction is known
2. Motor r/min is know
3. Motor Wk2
4. Load Wk2
5. graph of motor and load speed-torque characteristics
graphical approach might be used based on the simplified formula:
t(s)=[Wk**2(r/min1 - r/min2)x2xPI]/(60g x Tn), in seconds
or
t(s)=[Wk**2(r/min1 - r/min2)x2xPI]/(308 x Tn), in seconds
Wk**2 is inertia=(motor Wk2 + load Wk2)
R/min are RPM
Tn is the net average accelerating torque between rev/min1 and rev/min2
RE: Acceleration time
This thread would have been unnecessary if WR^2 (GD^2) were known. Esvhv said he wanted to find t(s), but he needed other data. The other data needed was WR^2.
RE: Acceleration time
But using this idea yields only the motor inertia, I require the load as well
Any suggestions???
In addition you quote the 3 second figure for a random motor but that is the range I am looking at do you have any other data
RE: Acceleration time
If other than a compressor, than use the NEMA tables referenced by Electricpete!
RE: Acceleration time
Earlier, Electricpete posted a NEMA MG-series standard that covers the calculation of "load" WR^2 values based on a known motor horsepower. Of course it will have to be converted to GD^2. But, it should provide you with the last bit of data you need. If the NEMA data-base is unavailable to you, let us know!
RE: Acceleration time
One note - If you use the NEMA maximum load inertia limit that I provided, you'll get an upper-bound for the inertia. That will give you an upper bound for the starting time. (Actual load inertia and therefore starting time may be much lower.)
RE: Acceleration time
Your conclusion is valid only if the actual parameters are known. Remember my approach only provides Esvhv with a first-pass calculation... just to get him up to speed (excuse the pun). Furthermore, it assumes that the motor is designed per NEMA standards!
BTW, the data I collected came from a myriad of manufacturers (in alphabetical order so as to preclude preference) including ACEC, AEG, AEI, Allis-Chalmers, Ansaldo, ASEA & Brown-Boveri (now ABB), Electric-Machinery, GE, GEC, Louis-Allis, Siemens, Westinghouse, and other lesser known manufacturers from other parts of the world. (Pity, that many of disappeared!)
RE: Acceleration time
Secondly how do I convert WR^2 values to GD^2,
RE: Acceleration time
It gets curiouser and curiouser. How did you obtain the motor's rating, and speed-torque curves for both motor and load, but not have the PD^2 parameters? What is the application?
RE: Acceleration time
If I obtain the max inertia value from the NEMA tables listed above, I would have to scale it down to a reasonable value. Would the amount of scaling depend upon the type of load i.e. a fan or pump.
Any other suggestion???
RE: Acceleration time
Jbartos,
This thread would have been unnecessary if WR^2 (GD^2) were known.
///Not quite. The needed data identification according to industry standards would be needed. As you very well know, there are myriad of various data available with very little explanations about their context.\\\
Esvhv said he wanted to find t(s), but he needed other data.
///See my comment above.\\\
The other data needed was WR^2.
///This is what I presented in general from IEEE Std 399. This standard assumes that the motor and load manufacturers will be providing these data since they are the correct and accurate source to provide them.\\\
RE: Acceleration time
I have two torque speed curves, one showing the motor torque the other load torque. But I need to find the Acceleration time; I have the true torque values along each line in n-m and the speed in rad/s. In addition I have the kW rating of the motor.
///The idea about the kW size would be helpful since from responsibility standpoint. Small and inexpensive motor related to inexpensive process could be set by some approximations and empirical information from this Forum. However, larger motor and more responsible application would be much better to do with the motor and load manufacturer tech support. In fact, this is almost requirement in many responsible larger motor applications.\\\
But I do not have any other data.
///This would imply that you are dealing with some smaller motor sizes that may have their data estimated or approximated.\\\
Is it possible to find the Acceleration time, or an approximation for it.
///It is usually being done over industry standards and catalog/spec data sheets for motors and loads.\\\
Help would be much appreciated
///Nameplate data would have been helpful.\\\
RE: Acceleration time
The integration of 1/MT - LT has been completed and all I need is a means of obtaining the WR^2 value, or a totally different means of finding the acceleration time without using the inertia values
RE: Acceleration time
http://www.nema.org/index_nema.cfm/1427/8672E77E-D3BC-494F-A0D0CE6E55B99A74/
Table 45 gives those MAXimum load inertia's by motor speed and horsepower.
Estimated Motor Rotor Inertia for Dynamic Braking is not given in the above document, it is in NEMA MG-1-2002 Section 14.46. (This standard costs money). But section 14.46 only contains a formula (the one above), not a table.
RE: Acceleration time
RE: Acceleration time
Here is the rest of the puzzle useful in your mathematical pilgrimage to determine acceleration time for the 10MW (13,600 Hp), 2-pole motor:
Load Wk^2 presented in NEMA Std MG 1-20.42, covering only 60-Hz machines, is:
Load Wk^2 = AxB-CxD, lb(f)-ft^2 units, where,
B = [(Hp^0.95)/(rpm/1000)^2.4]
C = [(Hp^1.80]/(rpm/1000)^1.8]
To convert the above Wk^2, in lb(f)-ft^2 units, to GD^2, in kg(f)-mt^2 units, multiply by the factor K, where,
K = 4.41E-02
The NEMA caveat is that this calculation may not be applicable for all Hp's not shown in their table.
Now you have all the parameters, Hp, Tl, Tm, motor GD^2, and, load GD^2. This procedure will provide you with a "first-pass" determination of acceleration time, ta.
RE: Acceleration time
The 'A' & 'D' constants missed the final cut. However, Electricpete had given 'A'. Repeating here:
A = 24 for 300 to 1800 rpm machines, and 27 for 3600 rpm.
The 'D' constant is 6.85E-02.
RE: Acceleration time
Please help me.I must have missed something that everybody seems to have seen.
You didn't mention the type of starting for this motor.Or the type of motor for that matter.Is it across the line start?VFD application,constant torque or variable torque?
The torque rating of the motor is normally specified taking the load torque in consideration.If this particular motor develops sufficient torque to accelerate the load without tripping and do it often, than its accelerating torque and time are of no concern.Caveat "Most times"
By the way,moment of inertia is usually stamped on most motors nameplate.The load Inertia might be a problem.
I believe all the good information provided by everybody should help you run this motor and I might add it help me as well.
Thank you all
GusD
RE: Acceleration time