When we need to calculate the theoretical value of MAF (air flow), I think it will be very helpful to use mathematical channels and some mathematical skills to calculate.
For all measurements and calculations, accuracy is very important, and when we use math channels for raw data, there are always a variety of variables. Through the introduction of this article, it will help us minimize the uncertainty caused by the mathematical channels and filter application methods.
What we are going to introduce is a 1.8-liter four-cylinder, naturally aspirated Toyota Celica engine (engine code 2ZZ-GE), focusing on the relationship between crankshaft sensor, throttle position and MAF during the process from idling to WOT.
Figure 1 Signal capture
In order to accurately measure the maximum engine speed during WOT, I amplified the voltage signal peak point in the A channel to facilitate the use of a time scale to measure the maximum engine speed. In addition, I also added the mathematical channel crank (A, 36) to draw the engine speed curve. (Note: When measuring the inductive crankshaft sensor signal, the voltage signal amplitude increases in proportion to the engine speed.)
For the introduction of the crank math channel, you can jump to the following blog post: Crank math channel draws RPM curve
Figure 2 crank math channel
As we can see in Figure 2, when using the time scale method on the left (6811 rpm) and the crank math channel on the right (6998 rpm), there will be differences in the measured values at higher engine speeds.
There are those "annoying spikes" in the A channel signal, and the Picoscope software will immediately detect a sharp increase in signal frequency when there is a missing tooth. The crank math channel does not record data when the missing tooth passes through the crankshaft sensor, so the missing tooth problem is solved. When the remaining teeth continue to work normally, the crank math channel will continuously display data.
By using the filtering function of the math channel, we can deal with the "annoying spikes" in the crank math channel. If you create a LowPass (60/36 *freq(A), 8) math channel, the displayed waveform will automatically use an 8 Hz low-pass filter.
Figure 3 The filtered rpm channel
Figure 3 we can clearly draw the engine speed curve, and will not generate spikes.
We can compare the crank math channel with the filtered speed math channel, as shown in Figure 4.
Figure 4 Crank and filter channel
Another math channel, LowPass (A, 8), applies an 8 Hz low-pass filter to the A channel, which can eliminate the spikes of the A channel signal for observation, but it will sacrifice some signal amplitude accuracy.
At the beginning, the maximum engine speed measured by the time scale was 6811 rpm, but the LowPass (A, 8) math channel measured 6547 rpm, a difference of 260 rpm.
If you only need to observe the engine speed, LowPass (A, 8) is a suitable mathematical channel, but if you want to calculate the theoretical air flow, you need an accurate rpm peak. This requires us to use the measured value of the math channel to be closer to the measured value obtained with the time ruler.
In fact, by modifying the low-pass filter frequency in the math channel, we can measure the accurate rpm peak value. We create a new math channel LowPass (60/36 * freq(A), 50). Because it contains a 50 Hz low-pass filter, our rpm peak value is more accurate (6807 rpm), and the spike interference is also minimal . According to the different types of crankshaft sensors in actual applications, we need to try different frequencies repeatedly to set the most appropriate low-pass filter.
Figure 5 Channels with increased filtering frequency
Now that we have an accurate mathematical channel, which can measure the accurate rpm peak value, we can continue to calculate the theoretical MAF.
Calculate the theoretical MAF value: MAF=(RPM*single cylinder displacement)/(60*the number of intake strokes produced by one revolution of the crankshaft). There are many ways to calculate the MAF value. According to the following steps, you can get the theoretical MAF of a naturally aspirated engine (assuming WOT).
Example: Celica uses a 1.8L four-cylinder 4-stroke naturally aspirated engine. Assuming that the engine is now running at 3000 rpm (WOT), the consumed air flow can be calculated as follows:
3000 RPM / 60 = 50 revolutions per second (Hz)
For a four-cylinder engine, each revolution of the crankshaft produces 2 intake strokes. Therefore, 50 revolutions per second * 2 = 100 intake strokes per second.
Intake volume per intake stroke = 1.8L/4 cylinders = 0.45L (450 cc) per cylinder.
100 intake strokes per second*0.45L=45L per second
Note: The density of air at sea level is about 1g/L (depending on pressure and temperature).
Therefore, 45 liters per second is approximately 45 grams per second (45 g/sec).
Having said that, the aerodynamic calculations are based on calculations at sea level around 15 degrees Celsius, when the air density is 1.223kg/m3 or 1.223g/L. So here, we multiply 45 liters per second by 1.223 to get 55.035 gm/s. It should be noted that all the above conditions assume that the engine's inflation efficiency (VE) is 100% . But in fact, the charging efficiency is about 90% at the maximum engine torque (the average range is 86%-88%).
To calculate the theoretical MAF for a four-cylinder engine, the formula for the mathematical channel is as follows:
LowPass (60/36 * freq (A), 50)/60/2*1.8 (air density is 1g/L):
LowPass (60/36 * freq(A), 50)/60/2*1.8*1.223 (air density is 1.223g/L).
Figure 6 MAF math channel
Now we draw the theoretical MAF in the entire speed range according to the two air densities (assuming VE is 100%). Here I ask a question worth thinking about, which air density (1 gm/ L or 1.223 gm/ L ) does the vehicle manufacturer use ? Which of these will appear in the MAF value they provide data in it ?
Then we talk about the calculation of VE. Regardless of the calculation skills or mathematical formulas, calculating VE is very challenging, because the complexity of intake manifold configuration, throttle position, valve duration/lift and aerodynamics cannot be summed up by a mathematical formula. However, we can use air flow data in the approximate calculation of VE.
We cannot assume that the engine has always been 100% VE, but if the engine VE is assumed to be 100% in the calculation of the air flow formula, then the actual MAF value is obtained through the scanning tool. The ratio of the theoretical MAF value to the actual MAF value is the approximate value of VE. . (It is assumed that the air flow meter is operating normally, there is no air leakage, and the engine has no performance problems.)
In Figure 7, the mathematical channel 60/36 * freq (A) measured the peak rpm of 7031 rpm and the theoretical MAF of 106.3gm/sec (assuming that the VE is 100% and the air density is 1gm/L measured). Interestingly, the MAF value is not 0 at the peak rpm, but the throttle is already fully closed! This may be caused by the fact that the engine speed will not drop immediately when the throttle is closed. Please remember that we are the root According rpm peak to calculate the theoretical MAF 's .
Figure 7 Waveform analysis
The scanning tool shows that MAF is 111.85 gm/sec at 7021 rpm, as shown in Figure 8. If we calculate these numbers now, the MAF calculated by the oscilloscope is 106.3 gm/sec, while the MAF reported by the scanning tool is 111.85 gm/sec, and the speeds of the two are similar. 111.85 / 106.3 =1.05*100%=105%, the inflation efficiency (VE) is 105%, which is simply impossible !
Figure 8 Scanning data
Although the engine uses VVT-iL "variable valve timing and lift" (valve lift increases at high speeds), its charging efficiency will certainly not exceed 100%, and it is still on the premise of no air leakage. If we calculate the MAF with 1.223 g / L now , maybe the VE will not exceed 100%.
Modify the MAF calculated by the oscilloscope to 106.3g/s*1.223=130g/s, the MAF reported by the scanning tool is 111.85g/s, 111.85/130=0.8604*100%=86.04%, and the actual inflation efficiency is 86.04%.
Therefore, we can conclude that in this case, the car manufacturer calculates the theoretical MAF value based on an air density of 1.223 g / L . To sum up, if we know the engine speed, the number of cylinders and the engine capacity, we can calculate the theoretical MAF.
We can also add the last correction factor to the math channel—VE takes an average of 88%. If the mathematical formula LowPass (60/36 * freq(A), 50)/60/2*1.8* is used in the case study 1.223*0.88, when we calculate the MAF value, we assume that VE is 88% instead of 100%: 130 gm / sec * 0.88 = 114.4 gm / sec (scan tool reading = 111.85 gm / sec). I'm not sure if this math channel is helpful, but based on the theoretical MAF calculated by 100% VE and the MAF reported by the scanning tool, it is very useful to calculate the actual approximate VE (after capture) based on their ratio.
The psdata file can be downloaded from the Hongke pico oscilloscope forum , hope it will be useful to you!