Injector Dynamic Range

[Ed Lansinger]

Peter wrote:

>At 01:43 PM 3/17/95 EST-11, DIY_EFI at coulomb.eng.ohio-state.edu wrote:
>>I have been thinking about some of the issues regarding EFI, and I 
>>was wondering if anyone has some ideas about the dynamic range of 
>>fuel injectors:  If it is around 48dB (ie. 256:1) 
>
>
>Thats an unusual approach! 
>
>The answer is that under 1.5 mS opening time the fuel flow is undefinable
>and conversely it takes 1.5 mS to shut and during that time the fuel fuel is
>undefinable. At 1 mS the injector does not open at all and if the close
>pulse is 1 mS or less the injector won't close. The dynamic range depends
>upon the PRF or engine speed. An 8 bit counter would work satisfactorily and
>most early computers used 8 bits but as 16 bits is almost as easy to get and
>use, more is better
>
>Peter

I recommend reading the paper "Non-Linearity at Low Flow Rates from Electro-magnetic 
Fuel Injector" by Nomura and Irino, JSAE Review, Vol. 8, No. 4.  This paper clears up 
many issues.  It references an SAE paper I've never read but could be easier to find, 
namely "A General Model for Solenoid Fuel Injector Dynamics", by Smith and Spinweber, 
SAE Paper 800508, 1980.

First, Peter is either talking about an injector type with which I am umfamiliar or his 
understanding of how injectors work is mistaken.  Both saturated-circuit and 
peak-and-hold injectors open when current flows through them and then close when the 
current flow is stopped.  They do not "toggle", i.e. they do not go open at an open 
pulse and then require a "close pulse" to close.  In regards to the statements about 1.5 
msec opening/closing times, this is an oversimplified view.  The "open time" ("To") (and 
here I quote from Nomura and Irino) is the "Time elapsed in milliseconds to completely 
open after receiving the 'fuel ON' command".  For some injectors To may be 1.5msec, but 
I have heard of others being in the sub-0.7msec range.  Fuel is certainly flowing while 
the pintle is moving to its open postion, although there may be a delay between when the 
current begins to flow and when the pintle retracts appreciably.  The "close time" 
("Tc") is the "Time required in milliseconds to close the valve and shut off fuel flow 
after receiving the 'fuel OFF' command" (i.e. after the current flow is turned off).  
Again, fuel still flows during this time.  The injector is assumed to be fully open 
before closing in measuring Tc.  If the injector was not fully open, it takes less time 
for it to close.  It is true that with sufficiently short pulses no pintle movement 
occurs; Nomura and Irino calculate (for a hypothetical peak-and-hold injector) that this 
 happens with pulse widths below 0.5msec.  The biggest factor here seems to be the 
simple fact that it takes time for current to build up in the solenoid due to 
inductance.

The reason the "oversimplified" view is useful is that, if you never operate the 
injector below a certain minimum pulse width, you can consider the fuel flow during the 
To and Tc periods to be constant regardless of total pulse width.  This lets you compute 
your flow with the simple equation f=mt+c, where c is the amount of fuel that flows 
during To and Tc, m is the flow rate, and t is the time the injector is commanded open 
beyond To.  You can still operate the injector at smaller pulse widths, but you get into 
a non-linear region where f=mt+c just doesn't apply.  Nomura and Irino's paper 
characterizes this non-linear region.  They start off with an interesting graph of a 
"typical" injector.  For this injector, the linear region covers pulse widths from about 
1.5 msec to about 9.2 msec.  As the pulse width grows larger than 9.2 msec, the flow 
rate in volume/unit time actually increases.  As the pulse width shrinks smaller than 
1.5 msec, the flow rate first decreases, then increases substantially, finally 
decreasing once more.  In this graph, the amount of fuel injected with a 1msec pulse is 
perhaps only 25% of the amount injected with a 1.5msec pulse, but the amount injected 
with a 0.7msec pulse is actually almost 50% more than with a 1.5msec pulse.  I wouldn't 
take the exact values too seriously, because I'm eyeballing them from a graph and this 
injector may have been chosen because it exaggerates the features.  The point of the 
paper is that the shape of the pulse width vs. flow curve, including the non-linear 
regions, is a characteristic of all injectors (peak-and-hold and saturated-circuit).  
You'll need to read the paper to get all the info, but here's the summary:

"Non-linearity at low flow rates can be divided into two ranges, each with its own 
cause.  Non-linearity at the lowest flow range is caused by the bounce of the needle 
when it collides with the maximum lift stopper.  At the next lowest flow range, 
non-linearity is a result of the effect of residual magnetic force after receiving the 
"fuel OFF" command."

Getting back to the original question about dynamic range, Nomura and Irino reference 
the term "dynamic flow range" which is essentially defined as the linear range 
(actually, the range in which flow is no more than 5% off from the linearized flow 
curve; in the example above, this range appears to be 1.5-9.2msec).  This isn't dynamic 
range in the sense of the original question.  The original question basically asks "how 
many distinguishable pulse widths are there between 1.5 and 9.2 msec (or, for that 
matter, between 0 and a lot)?"  You can imagine that pulse widths of 2.000000msec and 
2.000001msec might not produce measurably different quantities of fuel due to mechanical 
noise or whatever.  You can also imagine that even if the fuel injector did deliver 
measurably different quantities of fuel the difference would be utterly washed out in 
the "noise" of fuel condensing on the walls, evaportating out the ports, etc.

Nomura and Irino don't address this issue.  It is a function of the signal/noise ratio 
of the injector as the original questioner anticipated.  I personally don't know the 
answer, either.  I do know that other factors besides signal/noise ratio of the injector 
fuel flow rate (i.e. fuel pressure fluctuations, ineffective atomization/vaporization, 
manifold wetting, mass transport delays, mixing, charge dilution, etc.) will have an 
effect.  My unsubstantiated guess is that those things will be the limiting factors in 
just how many bits you could meaningfully use to time pulse width, not noise due to the 
injector itself.  Eight bits does work.  Sixteen bits sounds fine to me.  Thirty-two?  
Just how big are the molecules to begin with?

-------------------------------------------------------
Ed Lansinger
General Motors Powertrain
Powertrain Control Center
Premium V Software & Calibration Group
Milford Proving Ground, Milford, MI
elansi01 at mpg.gmpt.gmeds.com  8-341-3049  (810) 684-3049
-------------------------------------------------------