We start with a non-intrusive design of a force compression rod with indirect mechanical access to the combustion chamber (see Fig. 1a). The robust and massive rod-like sensor geometry will be compressed by the cylinder head deformation caused by pressure evolution in the cylinder. Highly sensitive foil strain gauges (Vollberg et al., 2015) are placed on the rod at a distance of approx. 2 cm from the combustion chamber to reduce the temperature level. By means of structural finite-element (FE) analysis performed with COMSOL Multiphysics, we evaluate suitable shapes of the rod for the application of strain gauges. As material the stainless steel PH 13-8 Mo (1.4534) was selected, being a high-strength alloy with a Young modulus of 210 GPa, known as a good steel for force transducers and excellent temperature-stable mechanical properties. By variation in different designs of the rod's front end (e.g. reducing the diameter, introduction of a stud hole), the best geometry we found is a sine-wave-like form with a phase shift of 180∘ for two opposite sides, depicted in Fig. 2a. The maximum diameter is 8 mm and the thinnest part is approx. 3.9 mm. Upon a force F equivalent to a pressure of 250 bar, applied on the tip of the rod, the geometry develops a negative strain of -0.34‰ (blue zones in Fig. 2b) and a mechanical stress of σ≈610 MPa on the surface of the contour (positions at R1, R2 in Fig. 2a). Additionally, there are areas with almost no strain (positions at R3, R4 in Fig. 2a and red zones in Fig. 2b). By having locations with compression and others without deformation, the geometry is suitable for foil strain gauge application. To take advantage of highly sensitive foil strain gauges, applied onto zones as illustrated in Fig. 2a, a very robust design of the rod was possible, attaining a compressive strain of only a third compared to typical strain gauge applications.

The thin film sensor materials are described elsewhere (Vollberg et al., 2015; Schultes et al., 2018; Schwebke et al., 2018). In brief, the backing material of the strain gauges is a 50 µm thick polyimide (PI) foil to ensure a good electrical insulation to the steel. The PI foil is coated with a highly strain-sensitive thin film in a combined plasma-enhanced vapour deposition process (PECVD). The thin film with a thickness of approx. 100 nm consists of metal clusters and columns of NiCr embedded in a graphite-like carbon matrix. The strain sensitivity (gauge factor) of such a sensor film is enhanced by a factor of approx. 5 compared to commercially available metal foil strain gauges. Simultaneously the temperature dependency is low. The sensor layer is structured by an ultrashort pulsed UV-laser system that allows the film to be removed by cold ablation without damaging the PI foil underneath (Langosch et al., 2015). To ensure electrical connection an additional multilayer thin film (NiCr/Ni/Au) is partially sputtered onto the designated contact pad areas. In a final step a covering PI foil is laminated over the strain gauges to prevent damaging. As a result of the FE analysis the active area of the strain gauge should be 1.3 mm2. With a structure path width of 200 µm and a separation of 30 µm between the conductive lines, we designed six parallel paths with a total resistance of approx. 5 kΩ. This is a good compromise between power consumption of the bridge and electrical noise. The thin film strain gauges are glued just as well-known commercial gauges are, with hot curing epoxide resin (M-Bond 610, Vishay) on the intended areas. After curing, the strain gauges were wire connected by soldering with a high-temperature solder (Solder HMP, P/N 610128, BLH).

An intrusive sensor design was developed as well. The concept uses membrane elements (Fig. 3a), mounted at the front end of a tube-like structure with direct access to the pressure inside the cylinder. The measuring elements either consist of a ceramic material based on zirconia or stainless steel with the relevant parameters summarized in Table 2. Both materials offer good mechanical properties at elevated temperatures and hence enable direct in-cylinder pressure measurement. To acquire information about the effective temperature level on the membranes, we first designed temperature-sensitive thin film resistors on the respective elements. Operating the combustion engine at different power levels, we thus were capable of measuring both the maximum temperature and the temperature gradient across the membranes. These results were also useful to conduct and verify the thermal–structural FE analysis, presented in Sect. 3.1.

To determine the temperature level of the different concepts, prototypes were equipped with temperature sensors and mounted in the diesel test bench, while operating the engine at maximum power (3600 rpm at 200 Nm torque). For the non-intrusive force compression rod, a temperature of approx. 120 ∘C was measured by means of a PT1000 sensor. This result is coherent with the mentioned arguments, as the sensor element is placed 2 cm from the combustion chamber and excessive heat is effectively dissipated to cooled engine parts.

The temperature level of the intrusive membrane-type pressure sensors depends on the applied materials – mainly on their thermal conductivity. With the small zirconia element, a temperature of about 295±5 ∘C was measured by means of a thin film resistor integrating the temperature across the membrane. The temperature varies with the engine coolant temperature in a range of ±5 K. The inner-cyclic variation during one combustion cycle is less than 1 K, due to the averaging measuring structure and the slow temperature response behaviour of the ceramic's low heat conduction. To simulate the temperature conditions for the intrusive membranes, the measured data were used to establish a thermal FE model, considering the specific geometries. As boundary conditions, the surfaces of the ceramic element were kept on assumed temperature levels as depicted in Fig. 7a. A periodic heat intake onto the element was simulated as a pulse of triangle shape with maximum heat flux derived from Parra (Parra, 2018) and a pulse width corresponding to a pressure curve at 3600 rpm (heat flux at maximum: 1 MW m-2, pulse width: 3 ms, repetition time: 33.33 ms). The pulse form was adjusted by a scaling factor of 0.75 and the cylinder head temperature was put to 180 ∘C to match the simulation output to the measured temperature of 295 ∘C on the ceramic membrane.

Besides the average temperature level of the membrane surface, the temperature gradient on the membrane is also important for the pressure sensor function. As the heat energy strikes the membrane, the material will absorb and conduct the heat. Obviously the predominant dissipation occurs at the circumferential contact surfaces (blue and black zones of Fig. 7a) into the clamped or welded housing. Consequentially, the membrane centre attains a higher temperature than the periphery. As the resistors of the Wheatstone bridge are arranged at the centre as well as in the periphery of the membrane, a signal would be generated depending on the temperature gradient and the films temperature coefficient (TCR). This signal would represent a distortion of the pressure signal.

The simulation of the zirconia membrane element yielded a temperature gradient of approx. 30 K from the inner gauge position at a radius of 0.25 mm to the outer strain gauge position at a radius of 1.4 mm, as illustrated in Fig. 7b. The result was then used to simulate the temperature deviation across the steel membrane by just changing the material parameters of zirconia to steel, while keeping the geometry as well as the boundary conditions constant. The thermal FE analysis for steel resulted in a significantly lower temperature level of only 187 ∘C at the membrane centre, also plotted in Fig. 7b. Simultaneously the temperature gradient is reduced to only 8 K at the appropriate strain gauge positions.

To verify the calculated results, a steel element equipped with two temperature resistors at the same locations as the pressure gauges was measured on the diesel test bench. This yielded 185±3 ∘C for the inner position and 177±3 ∘C for the outer position, also included in Fig. 7b. The values deviate only very slightly from the simulated data, also because the measured temperatures are averaged over a certain area. Thus, the thermal FE simulation delivers very plausible results. Hence, due to the higher temperature gradient, a higher temperature-dependent distortion of the pressure signal will be expected for the ceramic membrane sensor type. The lower overall temperature and the lower gradient favour the use of steel.

The three different sensor prototypes were first tested on the diesel engine at 1900 rpm and 150 Nm. The raw sensor signals were synchronously measured with a multichannel data acquisition unit (Q.brixx station, accuracy ±0.1 % FS, Gantner instruments) at a sampling rate of 5 kHz. The peak amplitude signals were scaled to the calibration data of the Beru PSG reference sensor to calculate the time-resolved pressure curves. As mentioned in the introduction, the reference sensor and the prototypes were mounted in different cylinders and hence experience the pressure peaks at different times. To obtain a better comparability of both signals, the data were manually shifted on the time axis until they overlap. By these means, exemplary pressure waveforms of one combustion cycle are depicted in Fig. 8 for each sensor concept in comparison with the reference signal.

In case of the non-intrusive force compression rod a total of two specimens were assembled, showing similar properties. The signal of one sensor is depicted in Fig. 8a. It matches that of the reference sensor very well. Even small details like the first pressure peak at 29 ms (milliseconds) are detected. Based on the calibration, the prototype has a sensitivity of approx. 7.9 µV (V bar)-1, corresponding to the predicted sensitivity of 6.9 µV (V bar)-1 by our structural FE analysis. A peculiar difference to the reference is a negative peak at 15 ms. At that time the neighbour cylinder exhibits its maximum combustion pressure. Hence, the pre-load force of the compression rod is reduced due to mechanical coupling, resulting in a negative peak. This inner-cyclic disturbance has the same frequency as the pressure signal. That may be a problem, if for instance in a multi-cylinder inline engine, a simultaneous ignition in one of the neighbouring cylinders occurs. In this circumstance, the negative peak would superimpose the pressure peak, leading to false pressure values.

Figure 8b showcases a signal gathered by means of the intrusive membrane-type sensor made of zirconia ceramics. The calibrated sensitivity is about 32 µV (V bar)-1, which is comparable to that obtained on the static pressure test bench (30.7 µV (V bar)-1 at 180 ∘C). This sensitivity is higher by a factor of 4 compared to the compression rod. The signal also shows an inner-cyclic deviation in the compression phase as well as in the expansion phase of the combustion cycle. The maximum deviation of approx. 11 bar occurs at 50 ms. This influence is likely caused by the heat strike onto the membrane during fuel burning and an associated inner-cyclic change in the thermal gradient across the membrane. Such thermal shock effects were also observed in other cylinder pressure sensor applications with piezoelectric elements, discussed by Hart (1999). Although the depicted pressure curve was taken at lower power, the changing temperature gradient produces a detrimental inner-cyclic signal distortion. In addition, due to the low thermal conductivity (2.5 W (m K)-1) of the zirconia material, the thermal FE analysis predicts a temperature gradient of up to 30 K from the centre to the membrane's periphery at maximum engine power. This probably results in a reduced zero-point stability over temperature. The amplitude of the distortion is determined by the temperature gradient and the TCR of the Wheatstone bridge resistors, being relatively high at 1200 ppm K-1 in this case. By adjusting the sputtering process, we were able to reduce the TCR to less than 100 ppm K-1, but this time the sensors failed for another reason. The thin films were destroyed at the operating temperature due to the starting oxygen ion conductivity of zirconia under DC excitation. As a bottom line we have to consider that zirconia elements are not suitable for this application.

The third sensor concept to be tested in the diesel engine, was the steel membrane type. Overall four sensors were built, which have comparable characteristics. The calibrated signal of one sensor is depicted in Fig. 8c. In this case a nearly perfect congruence with the reference signal is found, without any measurement artefacts. The sensitivity is approx. 87 µV (V bar)-1 and the maximum deviation is below 2 bar (< 1 % full scale). The higher sensitivity can be explained by the different geometric dimension of the steel membrane compared to the ceramic version and by an improved chromium thin film (Schwebke and Schultes, 2019) as strain gauge material. The thermal shock behaviour is obviously improved by using a steel membrane, a material with a relative high thermal conductivity of 16 W (m K)-1. Not only is the thermal shock error reduced, but also the maximum temperature on the membrane is significantly lower as we showed in Fig. 7b. Of the two membrane materials, steel is clearly preferred. Table 3 gives an overview of the main sensor characteristics of the examined sensor concepts.

In addition to the representation of one pressure peak (Fig. 8c), a sequence of several combustion cycles is depicted in Fig. 9, again with both sensors. The torque of the diesel engine was changed from 150 to 200 Nm at 3200 rpm in this course. Surprisingly, the change effectuates a pressure rise from one cycle to the next, as is obvious at 200 ms in the chart of Fig. 9. Both sensors deliver nearly identical signals. We point out that neither the amplitude nor the zero point exhibit a significant deviation of more than 2 bar. This behaviour supports the result that thermal influences are clearly reduced by the relatively high thermal conductivity of steel.

For an endurance test one of the steel membrane sensors was tested during 20 million cycles on a gasoline engine, as mentioned in Sect. 2. The sensor withstands the long-term stress without any malfunction and was characterized before and after the test with respect to zero point, sensitivity, linearity, and hysteresis.

In Fig. 10a, two measurements are plotted to compare the sensor characteristics before and after the long-term run. The measurements were carried out at 230 ∘C in the static pressure test bench. The sensitivity is increased by approx. 2 % after the test, probably due to thin film aging at higher temperatures. Other parameters like the bridge zero signal and the linearity error show no significant changes. Before and after the test, the linearity error is less than ±0.3 % full scale and the offset change is less than 0.3 mV V-1. These variations may also be caused by different mounting torques during the installation of the sensors. Figure 10b illustrates the linearity deviation after the long-term run of three consecutive measurements at 230 ∘C. In this type of diagram only the deviation from absolute linearity is plotted. The measurement indicates a good repeatability with respect to the sensitivity, linearity deviation of less than -0.3 %, and a hysteresis of approx. 0.25 %. This result shows a good performance of the steel membrane-type sensor at elevated temperature after the long-term test.