The proposed methodology has been assessed experimentally by means of a gasoline single-cylinder, 4-stroke turbocharged engine for a motorsport application i.e., the Formula SAE competition. To fulfill the requirements of the competition, the engine also had a 20 mm orifice restriction at the intake. The engine was equipped with double camshaft on the engine head; the main features are reported in
Table 1. Based on the engine characteristics, the effective operating range is shifted to pretty-high revolution speeds, being the maximum power obtained at approximately 8000 rpm. For the sake of this analysis, the analyzed revolution speeds were comprehended between 3000 rpm and 6000 rpm. Lower regimes were deemed not representative of the engine behavior, while higher ones were indeed achievable, but were not considered in this phase of the research for safety reasons at the test bench.
The mechanical stress was measured on one of the four head screws (i.e., the most accessible one, since two out of four screws were oil immersed, while the third was not accessible, needing mechanical modifications of the engine head) by means of a strain washer, whose main features are reported in
Table 2.
Figure 2 shows the strain washer installation between the screw head and the engine head. The strain washer chosen for the tests had a circular shape, with an internal hole of 10.5 mm diameter, an external diameter of 22 mm and a height of 10 mm. The strain washer was of piezoelectric type, therefore the dynamic measurement of the SW (relative sensor) did not depend on the applied preload. The sensor was installed under the left head screw on the intake side: this was indeed the only feasible solution on this type of engine without machining the head (
Figure 2). In fact, two head screws were located under the intake and exhaust camshafts, respectively, with relevant issues for the sensor operation, including high lubricant oil temperature, very narrow space for sensor installation and the need for realizing a dedicated path for the sensor cable. The last screw available was the left one on the exhaust side. It was indeed outside the engine head, but there was no space between the screw and the head surface for the installation of the sensor, needing an additional machining. To overcome this issue, since the sensor thickness was 10 mm, a new engine screw—10 mm longer respect to the original one—was designed and realized in order to properly assembly the engine head. In order to guarantee the same rigidity, all the screws have been lengthened by 10 mm and a spacer of 10 mm was installed between each screw and the head. This modification changed slightly the coupling force between the head and the cylinder but it did not affect the correct functioning of the engine. In further detail, the in-cylinder pressure was acquired first with the dynamic pressure sensor and the unmodified configuration; then, the acquisition was repeated with the SW and the new screws, noticing no modification of the engine behavior.
For the correct functioning, the engine screws must be screwed with a tightening torque of 55 Nm, which corresponds to a preload (
P) of 36 kN. Since the measurement range (
Mr) of the sensor was 44.48 kN the remaining dynamic rage (
Dr) for the measurement was:
The goal of the activity was to find a proper correlation able to link the SW to the PS signal. The data analysis was carried out on a set of experimental tests performed at the test bench of the Dept. of Industrial Engineering of the Università degli Studi di Firenze [
34], varying the engine speed (from 3000 to 6000 rpm) and the load (from low load to full load), in order to get a representative overview of the whole engine operating range.
Strain Washer Data Analysis
Figure 3 shows an example of the signal acquired by the strain washer. It can be noticed that the signal of the SW is slightly affected by noise. The noise is produced by the electronic coupling of the SW with the acquisition system. Based on a first numerical estimation, the maximum force acting on a single screw when the pressure is 80 bar (max in-cylinder pressure) is about 2.5 kN, so the remaining dynamic range was enough for the tests. The benchmark in-cylinder pressure was measured by a piezoelectric dynamic sensor, whose main features are reported in
Table 3.
The undesired background noise was sufficiently low and only affected the low-pressure area (intake and exhaust phases) of the thermodynamic cycle. Moreover, the average cycle, based on 100 consecutive cycles, resulted in a smoother trend without significant fluctuations. Nevertheless, in order to properly reconstruct the in-cylinder pressure from the strength signal, a frequency analysis of both PS and SW signals was performed. By considering the average cycle, the Fast Fourier Transformation (FFT) spectrum of the PS signal at different engine operating conditions is represented in
Figure 4. The main frequency of the PS signal is the combustion frequency which is directly related to the engine speed, consequently the magnitude of the spectrum is represented in function of the orders (expressed as multiples of the firing frequency). Upon examination of the results, it became apparent that over the 35th order (e.g., 1750 Hz at 6000 rpm) the amplitude of the PS spectrum was lower than 1% with respect to the amplitude of the firing frequency in the whole engine operating range.
Consequently, the useful spectrum content for the in-cylinder pressure analysis is assumed to lie under this order. Same considerations can be done considering the FFT analysis for different cycles at the same engine operating condition (
Figure 5): the spectrum shows differences in the low-frequency area due to the cycle to cycle variation but over the 35th order, the amplitude goes almost to zero.
According to the above, only the frequency content under the 35th order was taken into account also for the SW signal. The validity of this assumption can be readily noticed upon examination of
Figure 6, which depicts the FFT of the SW signal for different engine speed at full load. Moreover,
Figure 7 shows in light blue the reconstructed SW signal for a single engine cycle at 4000 rpm and full load, obtained by an inverse FFT of the original signal considering the first 35 orders: it is apparent that no relevant information was lost on the signal, with the only exception of the high-frequency background noise.
Stated the above,
Figure 8 compares directly the SW signal (N) and PS signal (bar) averaged on 100 consecutive cycles. The figure also displays: (a) the uncertainty of the strain washer; (b) the relative difference between the in-cylinder pressure measured with the PS and that derived from the SW; (c) IVO (Intake Valve Open), IVC (Intake Valve Close), EVO (Exhaust Valve Open), EVC (Exhaust Valve Close) points. In the figure, the SW signal is also graphically scaled in order to match the PS signal at the maximum pressure. It is apparent that the two signals are very similar in the angular region from 45° Before Top Death Center (BTDC) to 75° After Top Death Center (ATDC) and in the combustion area, while they differ considerably in the remaining area of the cycle. The reason of this discrepancy may be that the force measured by the SW during the intake and discharge phases is under the uncertainty of the sensor (1% of full-scale), which was equal to ±450 N. Nevertheless, the combustion phase is the main region of interest for the engine management, therefore the following analysis was carried out with special focus on this portion of the cycle.
Figure 8 also reports in green-shadowed areas the absolute relative difference in terms of pressure between the in-cylinder pressure measured directly with the PS and indirectly derived from the SW signal. From a perusal of the figure, one can readily notice that in the area of interest for the combustion analysis, the difference between the two signal is almost null; on the other hand, the difference during suction and discharge phases is not negligible.
As discussed, this behavior could be related to the higher uncertainty of the strain washer in that regions. However, the agreement found around the crank angles involving the combustion phase corroborates the suitability of the present method for implementation in real-time combustion analyses and control logics. In this view, to further assess the capabilities of the method, it is of interest to understand if this indirect methodology can be adopted to detect the arise of anomalous engine behaviors like knock, misfire or pre-ignition (see
Section 4).
Finally, in order to correlate the mechanical stress on an engine stud (
SW signal) with the in-cylinder pressure, the linear correlation reported by Equation (3) was here considered:
The values
and
(equal to 27.4 and 125.8, respectively, for the present test case) were calculated by considering two angular positions around the firing top dead center (between −5° − +10° Crank Angle (CA) around the Firing Top Death Center (FTDC)) where the strain washer signal is considered highly reliable. More in detail, since both the SW and the PS are relative sensors, to accurately calculate k and q parameters, it is necessary to set in the right way the absolute value of strength and pressure for both the SW and PS sensors during the measurement. Regarding the PS, the conventional assumption is that the average in-cylinder pressure in a window of ±5° CA around the Before Death Center (BDC) with the inlet valve open is equal to the intake pressure that is about 1 bar [
35]. In the same angular window, it is assumed that the average strength on the stud measured by the SW is equal to 0 N, this means that the mechanical apparatus, excluding the preload, is not stressed. Even for turbocharged engines, the strength at BDC can be considered negligible although the in-cylinder pressure at the BDC with the inlet valve opened can be higher than the ambient pressure.
The k and q values, in theory, are constant independently from the engine operating conditions and the choice of the two angular positions around the FTDC since the SW and the PS have a linear behavior. Actually, a dedicated sensitivity analysis purposefully carried out on the choice of these parameters highlighted that there are minimal variations (with maximum difference of about 5%) between k and q values calculated at different engine operating conditions; this is mainly due to the strong not-stationary nature of SW and PS measurements and to the uncertainty in the definition of the absolute value of both sensors. Therefore, once the k and q values are evaluated on different engine operating conditions, average values of k and q are considered to convert the strain washer signal in pressure during the experimental tests.