Acceleration time 3

[esvhv]

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

 

[jbartos]

Suggestion: Follow IEEE Std 399 (Brown Book) example for obtaining an acceleration curve

 

[electricpete]

You also need to know the total inertia J of the motor and load.

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.

 

[UKpete]

If you haven't got access to the brown book - going back to first principles, in SI units:

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)

 

[esvhv]

Yes thanks for that, Unfortunately I do not have the j value for the motor or the load, all I have is the KW rating the various torque values.

Why integrate between 0 and 2*pi*final speed ,and not just the 0 – final speed

 

[esvhv]

Is there a “fudge” or approximation to find the total inertia J that uses the KW rating or the various torque values??????

 

[UKpete]

esvhv - I only got as far as plotting the acceleration against speed, I haven't worked out the bit to find the acceleration time yet! It might be quicker to follow jbartos' suggestion.

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.

 

[electricpete]

I will mention the equation does come from the F=ma=m*dv/dt type relationship:

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.

 

[esvhv]

Thanks very much electricpete and Ukpete both your suggestions are very helpful,

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.

 

[electricpete]

Sorry, A=27 FOR 2-pole, 24 for others. A does not multiply the 2nd term. Once again this is only a max inertia limit (as can also be found in NEMA MG1 tables). Your load inertia may be much lower.

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

 

[UKpete]

esvhv - just for completeness, if you were using a graphical method you would have to plot 1/á i.e. the reciprocal of angular acceleration, against speed in rad/s. Then find the area under the curve between v=0 and v=max, units are seconds.

 

[esvhv]

Thanks to UKpete and electricpete

your help was much appreciated

 

[Shortstub]

You can determine inertia constants by plotting speed vs time curve, following de-energization!

 

[electricpete]

interesting idea, shortstub. That will require precise knowledge of the decellerating torque though. It seems to me that may not be an easy thing to predict. I think the major component would be rotating friction, right?

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.

 

[Shortstub]

Electricpete,

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!

 

[Shortstub]

Electricpete,

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.

 

[Modula2]

Most of my calculations must be done before a motor is built and installed. In other cases, very few customers want to pay for site testing. I think this is common. During system design stage, we would like to build it correct the first time, and not have to reconstruct on site after. It is reasonable to request and obtain valid engineering data on motor inertia and performance curves, and load inertia and starting torque curves. Much of that is calculated data, but is acceptable at that stage. Otherwise, someone is expecting you to guess at numbers and I hope it is that person(s) who accept the liability. I fix several large motor "fail-to-start" per year. Not being thorough on valid data is very common.

 

[electricpete]

I'm sure everyone agrees that inertia should be available from the equipment manufacturers. (If it's not, then put it in your spec and you'll get it).

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.

 

[Modula2]

Experimental determination of inertia by coasting curve has been well documented. For a brief outline see
"Control of Electrical Drives", by Leonhard.

 

[Shortstub]

esvhv,

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.